What happened to CSGnet?

Dick_Robertson · November 8, 2009, 8:37pm

[From Dick Robertson, 2009.11.08.1428CDT]

Hey, did CSGnet go out of business or move somewhere else when I wasn’t looking?

If there is anybody left here what do you think about how PCT might approach this new “field” of behavioral economics, as exemplified in the study I post here?

                                                 Behavioral Economics Study

A recent “New York Times Bestseller,” Predictably Irrational, by Dan Ariely, describes a host of experiments to establish all the ways that decision making displays “The hidden forces that shape our decisions.” Note that word, “forces.” Would those “forces” be examples of unconsciously identified (or selected-for-control”) controlled variables? “ Anyway, it seems like an interesting question—what is a person controlling that produces findings like Ariely got in experiments like the following?

On page 26 he introduces this experiment. “…if I asked you for the last two digits of your social security number…then asked you whether you would pay this number in dollars for a particular bottle of [1998 wine] would the mere suggestion of that number influence how much you would be willing to spend on wine? Sounds preposterous, doesn’t it? Well, wait until you see what happened to a group of MBA students at MIT …. “

Saying that he and a co-investigator were trying to prove “the existence of … “arbitrary coherence,” they asked 55 students to observe six objects (left list below) and fill out “… the last two digits of your social security number at the top of the [response sheet], and then write them again next to each of the items in the form of a price. [and then] When you are finished with that I want you to indicate on your sheets—with a simple yes or no—whether you would pay that amount for each of the products.” Next, they were to write down the minimum they would pay for each of the products. The last data were averaged for the five groups in the table.

(We assume that the SS-number groups were roughly even in terms of number of students in each, but we are not told that here.)

Results

“When I … analyzed the data… Did the digits from the SS numbers serve as anchors? Remarkably, they did.”

See the table. The consistency of increasing means in each field (with just two exceptions) seems rather impressive for soc. Sci. type of data, although the nudest correlations are typical, and suggest that a lot of subjects were far on each side of the mean.

But it raises what I think is an interesting question: What were the subjects controlling for that their so-called “bids” seemed influenced by the soc. Sec. numbers they wrote down just before making their “bids?”

                                                                 Range of last two digits of SS number

Products 00-19 20-39 40-59 60-79 80-99 Correlations

Cordless Trackball 8.64 11.82 13.45 21.18 26.18 0.42

Cordless Keyboard 16.09 26.82 29.27 34.55 55.64 0.52

Design Book 12.82 16.18 15.82 19.27 30.00 0.32

Chocolates 9.55 10.64 12.45 13.27 20.64 0.42

1998 Wine 8.64 14.45 12.55 15 45 27.91 0.33

1996 Wine 11.73 22.45 18.09 24.55 37.55 0.33

This work, along with the similar stuff for which Kahnemann and Tversky won the Nobel in economics is getting widespread attention, and apparently many people are found to follow the patterns determined for average persons in their various studies. How would a PCT study go about to identify the various CVs that different people might be controlling in these experiments (but also in real-life decisions they claim) that would produce the average results in these Casting Nets studies?

Best,

Dick R

rsmarken · November 9, 2009, 3:28am

[From Rick Marken (2009.11.08.1930)]

Dick Robertson (2009.11.08.1428CDT) –

Hey, did CSGnet go out of business or move somewhere else when I wasn’t looking?

No. I’ve just been busy so I haven’t had the time to say anything infuriating

If there is anybody left here what do you think about how PCT might approach this new “field” of behavioral economics, as exemplified in the study I post here?

I’d love to talk about this; indeed, I may be directing a student’s senior honors project on this topic (or something like it). I’ll read this over and try to come up with some comments ASAP.

Best

Rick

···

                                                 Behavioral Economics Study
A recent New York Times Bestseller, Predictably Irrational, by Dan Ariely, describes a host of experiments to establish all the ways that decision making displays The hidden forces that shape our decisions. Note that word, forces. Would those forces be examples of unconsciously identified (or selected-for-control) controlled variables? Anyway, it seems like an interesting questionwhat is a person controlling that produces findings like Ariely got in experiments like the following?

On page 26 he introduces this experiment. if I asked you for the last two digits of your social security numberthen asked you whether you would pay this number in dollars for a particular bottle of [1998 wine] would the mere suggestion of that number influence how much you would be willing to spend on wine? Sounds preposterous, doesnt it? Well, wait until you see what happened to a group of MBA students at MIT .

Saying that he and a co-investigator were trying to prove the existence of arbitrary coherence, they asked 55 students to observe six objects (left list below) and fill out the last two digits of your social security number at the top of the [response sheet], and then write them again next to each of the items in the form of a price. [and then] When you are finished with that I want you to indicate on your sheetswith a simple yes or nowhether you would pay that amount for each of the products. Next, they were to write down the minimum they would pay for each of the products. The last data were averaged for the five groups in the table.

(We assume that the SS-number groups were roughly even in terms of number of students in each, but we are not told that here.)

Results

When I analyzed the data Did the digits from the SS numbers serve as anchors? Remarkably, they did.

See the table. The consistency of increasing means in each field (with just two exceptions) seems rather impressive for soc. Sci. type of data, although the nudest correlations are typical, and suggest that a lot of subjects were far on each side of the mean.

But it raises what I think is an interesting question: What were the subjects controlling for that their so-called bids seemed influenced by the soc. Sec. numbers they wrote down just before making their bids?

                                                                 Range of last two digits of SS number

Products 00-19 20-39 40-59 60-79 80-99 Correlations

Cordless Trackball 8.64 11.82 13.45 21.18 26.18 0.42

Cordless Keyboard 16.09 26.82 29.27 34.55 55.64 0.52

Design Book 12.82 16.18 15.82 19.27 30.00 0.32

Chocolates 9.55 10.64 12.45 13.27 20.64 0.42

1998 Wine 8.64 14.45 12.55 15 45 27.91 0.33

1996 Wine 11.73 22.45 18.09 24.55 37.55 0.33

This work, along with the similar stuff for which Kahnemann and Tversky won the Nobel in economics is getting widespread attention, and apparently many people are found to follow the patterns determined for average persons in their various studies. How would a PCT study go about to identify the various CVs that different people might be controlling in these experiments (but also in real-life decisions they claim) that would produce the average results in these Casting Nets studies?

Best,

Dick R

–
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

Richard_H_Pfau · November 9, 2009, 2:20pm

From Richard Pfau (2009.11.09.9:19 EDT)

My take on the Behavioral Economics Study you provided centers around the idea of “priming” the Output Function response. That is, choosing the last 2 digits of the person’s social security number primed the person to act toward higher, more moderate, or lower numbers so that when an Output Function response was enacted by the person, the tendency (among some people at least, since the correlations were modest) was to offer a price affected by the primed number. That is, If their social security number was low, (some) individuals indicated a low minimum they would pay, and if the number was higher, they wrote a higher price (the number of people affected that way being enough to obtain the results you indicate).

The controlled variable need not have been affected at all; only the Output Function may have been affected as a result of the priming that occurred.

With Regards,

Rich Pfau

···

-----Original Message-----

From: Richard Marken rsmarken@GMAIL.COM

To: CSGNET@LISTSERV.ILLINOIS.EDU

Sent: Sun, Nov 8, 2009 10:28 pm

Subject: Re: What happened to CSGnet?

[From Rick Marken (2009.11.08.1930)]

Dick Robertson (2009.11.08.1428CDT) –

Hey, did CSGnet go out of business or move somewhere else when I wasn’t looking?

No. I’ve just been busy so I haven’t had the time to say anything infuriating

If there is anybody left here what do you think about how PCT might approach this new “field” of behavioral economics, as exemplified in the study I post here?

I’d love to talk about this; indeed, I may be directing a student’s senior honors project on this topic (or something like it). I’ll read this over and try to come up with some comments ASAP.

Best

Rick

                                                 Behavioral Economics Study
A recent âNew York Times Bestseller,â? Predictably Irrational, by Dan Ariely, describes a host of experiments to establish all the ways that decision making displays âThe hidden forces that shape our decisions.â? Note that word, âforces.â? Would those âforcesâ? be examples of unconsciously identified (or selected-for-controlâ?) controlled variables? â Anyway, it seems like an interesting questionwhat is a person controlling that produces findings likee Ariely got in experiments like the following?

On page 26 he introduces this experiment. âif I asked you for the last two digits of your social security nuumberthen asked you whether you would pay this number in dollarss for a particular bottle of [1998 wine] would the mere suggestion of that number influence how much you would be willing to spend on wine? Sounds preposterous, doesnât it? Well, wait until you see what happened to a group of MBA students at MIT â¦. â

Saying that he and a co-investigator were trying to prove âthe existence of âarbitrary coherence,â? they asked 55 students to observe six objects (left list below) and fill out â the last two digits of your social securiity number at the top of the [response sheet], and then write them again next to each of the items in the form of a price. [and then] When you are finished with that I want you to indicate on your sheetswith a simpple yes or nowhether you would pay that amount for each of the prooducts.â? Next, they were to write down the minimum they would pay for each of the products. The last data were averaged for the five groups in the table.

(We assume that the SS-number groups were roughly even in terms of number of students in each, but we are not told that here.)

Results

âWhen I analyzed the dataâ¦ Did the digits from the SS numbers serve as anchors? Remarkably, they did.â?

See the table. The consistency of increasing means in each field (with just two exceptions) seems rather impressive for soc. Sci. type of data, although the nudest correlations are typical, and suggest that a lot of subjects were far on each side of the mean.

But it raises what I think is an interesting question: What were the subjects controlling for that their so-called âbidsâ? seemed influenced by the soc. Sec. numbers they wrote down just before making their âbids?â?

                                                                 Range of last two digits of SS number

Products 00-19 20-39 40-59 60-79 80-99 Correlations

Cordless Trackball 8.64 11.82 13.45 21.18 26.18 0.42

Cordless Keyboard 16.09 26.82 29.27 34.55 55.64 0.52

Design Book 12.82 16.18 15.82 19.27 30.00 0.32

Chocolates 9.55 10.64 12.45 13.27 20.64 0.42

1998 Wine 8.64 14.45 12.55 15 45 27.91 0.33

1996 Wine 11.73 22.45 18.09 24.55 37.55 0.33

This work, along with the similar stuff for which Kahnemann and Tversky won the Nobel in economics is getting widespread attention, and apparently many people are found to follow the patterns determined for average persons in their various studies. How would a PCT study go about to identify the various CVs that different people might be controlling in these experiments (but also in real-life decisions they claim) that would produce the average results in these Casting Nets studies?

Best,

Dick R

–

Richard S. Marken PhD

rsmarken@gmail.com

www.mindreadings.com

rsmarken · November 9, 2009, 4:27pm

[From Rick Marken (2009.11.09.0830)]

Dick Robertson (2009.11.08.1428CDT)

A recent New York Times Bestseller, Predictably Irrational, by Dan Ariely, describes a host of experiments to establish all the ways that decision making displays The hidden forces that shape our decisions. Note that word, forces. Would those forces be examples of unconsciously identified (or selected-for-control) controlled variables? Anyway, it seems like an interesting questionwhat is a person controlling that produces findings like Ariely got in experiments like the following?

The first question I would have about this study is “why do an experiment like this in the first place”? Obviously, such an experiment is based on the assumption that external events (like the last 2 digits of one’s SS number) can “force” behavior (estimates of what one would pay for a product). So the methodology guarantees that, if there are any differences across conditions, one will see such results in S-R terms. The conclusion will be what it was: that the SS# stimuli serve as anchors for responses (estimates).

But we know from PCT that external stimuli don’t cause behavior; they won’t even seem to influence behavior unless they are a disturbance to a controlled variable. The fact that the average response go up as the SS# goes up suggests that for at least some subjects (not necessarily all, since we are dealing with averages) the SS# is a disturbance to some variable that is being controlled by the subject by giving higher estimates when the SS# is higher. So the controlled variable is probably something like: estimate/SS# = k. That is, some subjects must be controlling for making their estimates proportional to the last 2 digits of the SS#).

Why some subjects control for this is an interesting question; it probably has to do with trying to control for doing what the subject imagines that the experimenter wants them to control for. Most people who are put in experiments seem to want to cooperate with the experimenter; they control for being “sociable” (though I have had the occasional subject in my experiments controlling for being contentious).

I think what’s interesting about this experiment is that anyone in economics could possibly find it interesting.

Best

Rick

···

–
Richard S. Marken PhD
rsmarken@gmail.com

www.mindreadings.com

rsmarken · November 9, 2009, 6:18pm

[From Rick Marken (2009.11.09.1020)]

Richard Pfau (2009.11.09.9:19 EDT)

My problem with this explanation is that it still assumes that events in the environment (like the last 2 digits of an SS#) can have an effect, such as “priming”, on behavior. I think the SS# exists only as a perception for the subject and what the subject does about that perception is up to the subject.

Best

Rick

···

My take on the Behavioral Economics Study you provided centers around the idea of “priming” the Output Function response. That is, choosing the last 2 digits of the person’s social security number primed the person to act toward higher, more moderate, or lower numbers so that when an Output Function response was enacted by the person, the tendency (among some people at least, since the correlations were modest) was to offer a price affected by the primed number. That is, If their social security number was low, (some) individuals indicated a low minimum they would pay, and if the number was higher, they wrote a higher price (the number of people affected that way being enough to obtain the results you indicate).

The controlled variable need not have been affected at all; only the Output Function may have been affected as a result of the priming that occurred.

With Regards,

Rich Pfau

–
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

Richard_H_Pfau · November 9, 2009, 9:40pm

[From Richard Pfau (2009.11.09.1640 EDT)]

My problem with this explanation is that it still assumes that events in the environment (like the last 2 digits of an SS#) can have an effect, such as “priming”, on behavior. I think the SS# exists only as a perception for the subject and what the subject does about that perception is up to the subject.

[From Rick Marken (2009.11.09.1020)]
But events in the environment do have an effect on behavior don’t they? Such effects may be indirect, but they are effects nonetheless. For example, if you flew to a place 12,000 feet above sea level, you would not be (or could not be) nearly as active as at your normal lower altitude. You’d run a mile slower if at all, would probably sleep more, and so on (due to the lower oxygen levels in your blood). Similarly, an event such as an explosion nearby would affect your adrenaline levels (fight-or-flight/stress response), increasing your heart rate and blood pressure, preparing your body to cope with the situation in ways expained by PCT. But again, the explosion (an environmental event) has an effect or effects, at least some of which are indirect (adrenaline release, increased heart rate, …) with respect to your main Output Function behavior afterwards (which may now be carried out more swiftly, alertly, forcefully, for example).

In such a manner, I’m suggesting that perceived environmental events, such as being asked to recall the last 2 digits of your SS#, activate and prime related neural mechanisms, so that that those neural mechanisms temporarily become more sensitive and/or easier to activate (increasing the gain of those neural networks?), such that when an error signal occurs, those neural networks are more likely to be activated. Such priming seems to be an indirect environmental effect that can influence the mechanism associated with deciding which of a number of possible Output Function behaviors occurs – but doesn’t determine the behavior. (Just as oxygen levels and hormone levels resulting from environmental events and situations can indirectly influence behavior, but not directly determine what specific behavior occurs).

Such priming of neural networks doesn’t seem to conflict with PCT at all; the priming idea, if valid, simply helps to explain some PCT mechanisms a bit more.

With Regards,

Rich Pfau

rsmarken · November 10, 2009, 3:42pm

[From Rick Marken (2009.11.10.0740)]

Richard Pfau (2009.11.09.1640 EDT)–

[From Rick Marken (2009.11.09.1020)]

My problem with this explanation is that it still assumes that events in the environment (like the last 2 digits of an SS#) can have an effect, such as “priming”, on behavior. I think the SS# exists only as a perception for the subject and what the subject does about that perception is up to the subject.

But events in the environment do have an effect on behavior don’t they?

I’d have to say no, not according to PCT anyway. Environmental events have an effect on controlled variables, not directly on behavior (action).

Such effects may be indirect, but they are effects nonetheless.

OK, I’ll buy that, as long as we understand that the indirectness comes from the effect of the environment on controlled variables.

For example, if you flew to a place 12,000 feet above sea level, you would not be (or could not be) nearly as active as at your normal lower altitude. You’d run a mile slower if at all, would probably sleep more, and so on (due to the lower oxygen levels in your blood).

Yes, all these “effects” of altitude are the result of the disturbance to a controlled variable: oxygen level in the blood. When the air provides little oxygen per breath you compensate by acting in a way that takes less oxygen from the blood (you run more slowly, for example).

Similarly, an event such as an explosion nearby would affect your adrenaline levels (fight-or-flight/stress response), increasing your heart rate and blood pressure, preparing your body to cope with the situation in ways expained by PCT.

Yes, because of the effect of the explosion on a controlled variable: perception of safety. If you are not controlling for safety the explosion will have no effect on adrenaline secretion, heart rate or blood pressure.

But again, the explosion (an environmental event) has an effect or effects, at least some of which are indirect (adrenaline release, increased heart rate, …) with respect to your main Output Function behavior afterwards (which may now be carried out more swiftly, alertly, forcefully, for example).

I would say that the adrenaline release is part of the output driven by the error created when the explosion disturbed the controlled perception (safety), moving it away from its reference (safe).

In such a manner, I’m suggesting that perceived environmental events, such as being asked to recall the last 2 digits of your SS#, activate and prime related neural mechanisms, so that that those neural mechanisms temporarily become more sensitive and/or easier to activate (increasing the gain of those neural networks?), such that when an error signal occurs, those neural networks are more likely to be activated.

What you are suggesting is an S-R model of the effects of environmental events. That’s fine. It’s certainly a popular model but it’s not PCT.

Such priming seems to be an indirect environmental effect that can influence the mechanism associated with deciding which of a number of possible Output Function behaviors occurs

The apparent “priming effect” of SS# only occurs when the subject is controlling for making bids that are proportional to SS#. If the subject is not controlling for such a perception, the SS# has no apparent effect on bids; at least not in my admittedly limited bidding experience;-)

Such priming of neural networks doesn’t seem to conflict with PCT at all; the priming idea, if valid, simply helps to explain some PCT mechanisms a bit more.

As you’ve described it, such priming does conflict with PCT; it sounds like an S-R theory of the observed bidding behavior. My theory is that the apparent effect of SS# on bids results from the fact that subjects are controlling for something like a perception of the ratio bid/SS# = k. I think we need to set up an experiment to discriminate our two models.

Best

Rick

···

–
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

Dick_Robertson · November 10, 2009, 4:02pm

[From Dick Robertson,2009.11.10.0955CST]

[From Rick Marken (2009.11.10.0740)]

…

What you are suggesting is an S-R model of the effects of environmental events. That’s fine. It’s certainly a popular model but it’s not PCT.

Such priming seems to be an indirect environmental effect that can influence the mechanism associated with deciding which of a number of possible Output Function behaviors occurs

…

As you’ve described it, such priming does conflict with PCT; it sounds like an S-R theory of the observed bidding behavior. My theory is that the apparent effect of SS# on bids results from the fact that subjects are controlling for something like a perception of the ratio bid/SS# = k.

I think we need to set up an experiment to discriminate our two models.

Great! That was my question in the first place, minus the idea of testing between PCT and S/R models, but that is a terrific idea. I’d be glad to help gather data or in any other way I could, but I’m not up to designing the experiment, you are.

Best,

Dick R

Richard_H_Pfau · November 10, 2009, 4:53pm

[From Richard Pfau (2009.11.10.1153 EDT)]

[From Rick Marken (2009.11.10.0740)]

Richard Pfau (2009.11.09.1640 EDT)–

Such priming of neural networks doesn’t seem to conflict with PCT at all; the priming idea, if valid, simply helps to explain some PCT mechanisms a bit more.

As you’ve described it, such priming does conflict with PCT; it sounds like an S-R theory of the observed bidding behavior. My theory is that the apparent effect of SS# on bids results from the fact that subjects are controlling for something like a perception of the ratio bid/SS# = k. I think we need to set up an experiment to discriminate our two models.

Setting up an experiment is a reasonable idea. Perhaps one of our budding PhD students or other member of CSGNET might be interested. (Unfortunately, I’m in writing mode for the next year or two and am unable to do so). Someone working with students might add this to the list of possible PCT-related research projects.

With Regards,

Rich Pfau

MartinT · November 10, 2009, 7:45pm

[Martin Taylor 2009.11.10.12.06]

[From Rick Marken (2009.11.10.0740)]

My theory is that the apparent effect of SS# on bids results from the
fact that subjects are controlling for something like a perception of
the ratio bid/SS# = k.

Is there something in the reported data that would lead you to guess
that any subject is controlling for a relationship of any kind between
the SS# and the bid? Each subject has only one SS#, so how could any
subject control for such a ratio? All a subject can do is to bid on the
six different objects. It’s the relationship among bids across
different subjects that leads to the reported correlations. As Bill P.
has pointed out many times, it’s quite possible that the correlation
for each single subject might be in the opposite sense.

Nevertheless, there does seem to be something quite real going on.
Here’s a plot of the deviation of the log of the bid price from its
average for that object, as a function of the SS#. The 1, 2, 3, 4, 5
numbers on the abscissa represent the 20-number bins from 0-20 up to
80-99.

I find it hard to look at that plot and say that the Social Security
number has no effect on the bid price for any subject. The plots are so
similar for all six objects, and the range so exceeds the differences
among the objects, that you can even imagine you see an apparently
consistent end-effect deviation from linearity in the plot. Of course,
this is based on an average across subjects, so anything might differ
from one subject to the next, but the consistency of the plot across
subjects suggests that if there are differences in individual subjects’
effects, they are likely to be more a matter of scale than of kind.

The plot does not seem to suggest subjects controlled for a ratio
between SS# and bid price, because if they did, the curve would have
quite a different shape. The 0-20 bid price should be 1/3 of the 20-40
bid price (0.48 log units instead of about 1.3), whereas the 60-80 bid
price should be 7/9 of the 80-99 bid price (0.11 log units instead of
about 2.0).

If thinking about the SS# does affect the reference value for the bid
perception, it must do so by some way other than as a simple ratio.
What might the mechanism be? And what the function?

Martin

rsmarken · November 10, 2009, 8:51pm

[From Rick Marken (2009.11.10.1250)]

Richard Pfau (2009.11.10.1153 EDT)

Setting up an experiment is a reasonable idea.

If you (or one of your students) wants to set up the experiment to test your “priming” theory that would be great. Otherwise I don’t think it will get done. I’ve done enough experiments that demonstrate, in principle, (to me, anyway) that priming, as you seem to conceive it, doesn’t occur. If it occurs as Bill and Martin conceive it – the “prime” being incorporated as a perceptual aspect of the bid itself-- then it’s just good old control of perception; it’s just a different controlled variable than the one I suggested.

I think it’s always good to do research but I try to focus on studies that test basic principles of control. I think this SS# study is, as Bill said, only of interest to people who want to profit from some small influence an environmental variable might have on some behavior.

Best

Rick

···

–
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

rsmarken · November 10, 2009, 9:23pm

[From Rick Marken (2009.11.10.1320)]

Martin Taylor (2009.11.10.12.06)–

Rick Marken (2009.11.10.0740)–

My theory is that the apparent effect of SS# on bids results from the
fact that subjects are controlling for something like a perception of
the ratio bid/SS# = k.

Is there something in the reported data that would lead you to guess
that any subject is controlling for a relationship of any kind between
the SS# and the bid?

Sure. The fact that the bid increases with SS# suggests that subjects are controlling a relationship between the bid and SS#.

Each subject has only one SS#, so how could any
subject control for such a ratio?

This way. The reference ratio of bid/SS# is .2. My SS# (last 2 digits) is .55. If I bid 11 the perceived ratio of bid/SS# will be at the reference.

All a subject can do is to bid on the
six different objects. It’s the relationship among bids across
different subjects that leads to the reported correlations.

The IV (disturbance to the controlled variable) is the size of the SS#, which differs across individuals. If some subjects are controlling for bid/SS# at about the same reference, then the bids will be higher, on average, for Ss with high SS#s compared to those with low SS#s, which is exactly what is seen in the data.

As Bill P.
has pointed out many times, it’s quite possible that the correlation
for each single subject might be in the opposite sense.

That’ seems unlikely to be the case here. But it wouldn’t matter anyway. We are basing our thoughts about what might be controlled based on what is observed, not on what might be observed.

Nevertheless, there does seem to be something quite real going on.

I know. I think some subjects are really trying to control for a relationship between bid and SS#.

Here’s a plot of the deviation of the log of the bid price from its
average for that object, as a function of the SS#. The 1, 2, 3, 4, 5
numbers on the abscissa represent the 20-number bins from 0-20 up to
80-99.

Nice!

I find it hard to look at that plot and say that the Social Security
number has no effect on the bid price for any subject.

I know. That’s the behavioral illusion for you. But as you know from PCT the apparent effect of an environmental variable (SS# in this case) on behavior (bid) is actually the control system’s resistance to a disturbance of a controlled variable caused by the IV (SS# in this case) and compensated for by the DV (bid).

The plot does not seem to suggest subjects controlled for a ratio
between SS# and bid price, because if they did, the curve would have
quite a different shape. The 0-20 bid price should be 1/3 of the 20-40
bid price (0.48 log units instead of about 1.3), whereas the 60-80 bid
price should be 7/9 of the 80-99 bid price (0.11 log units instead of
about 2.0).

I don’t understand on what basis this prediction is made. I can predict these data quite well under the assumption that subjects are controlling the bid/SS# ratio at about the same reference. The exact shape of the curves is bound to be a little bumpy, since what is plotted are averages and not all subjects will be controlling this relationship and those who are will not be controlling it at the same reference level. But if there are at least some bid/SS# controllers in each group controlling relative to about the same reference you will see a monotonic increase in the curves for each product.

If thinking about the SS# does affect the reference value for the bid
perception, it must do so by some way other than as a simple ratio.
What might the mechanism be? And what the function?

I’m not saying that SS# affects the reference for bid perception. I’m saying (hypothesizing, really) that the controlled variable is bid/SS# = k; k is the controlled variable; variations in SS# are a disturbance to that variable. The reference for that variable is unknown, but it looks like it’s about .2 or so.

Best

Rick

···

–
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

MartinT · November 11, 2009, 5:49am

[Martin Taylor 2009.11.10.23.48]

[From Rick Marken (2009.11.10.1320)]

Martin Taylor
(2009.11.10.12.06)–

Rick Marken (2009.11.10.0740)–

My theory is that the apparent effect of SS# on bids
results from the
fact that subjects are controlling for something like a perception of
the ratio bid/SS# = k.

Is there something in the reported data that would lead you to guess
that any subject is controlling for a relationship of any kind between
the SS# and the bid?

Sure. The fact that the bid increases with SS# suggests that subjects
are controlling a relationship between the bid and SS#.

All right. In another message you accepted that another possibility is
that the perception of the magnitude of the number is what is changed
by thinking of the SS#, so let’s follow the idea that subjects are
controlling a relationship between the bid and the SS#. You suggest
that this relationship is, or is like, a ratio.

Each subject has only one
SS#, so how could any
subject control for such a ratio?

This way. The reference ratio of bid/SS# is .2. My SS# (last 2 digits)
is .55. If I bid 11 the perceived ratio of bid/SS# will be at the
reference.

Two questions.

Where does this reference ratio come from. In other words, what
perception is being controlled at some higher level that results in
some specific value for the reference ratio?
What is it about the different objects that disturbs this putative
higher level controlled perception to change that reference value? On
the assumption that the reference value averaged across subjects for a
specific object was fitted by value = k*SS# + constant, I get the
following values for k:

Trackball 0.2222

Keyboard 0.43415

Book 0.18725

Chocolate 0.12405

1998 Wine 0.1977

1996 Wine 0.2687

Those reference values for k range over a factor of about 3.5, so there
must be something about the specific objects that disturbs some
higher-level controlled perception in such a way that its output to the
reference input of the bid/SS# ratio control system varies over this
wide range. What about the objects might be perceived to produce that
disturbance?

All a subject can do is to
bid on the
six different objects. It’s the relationship among bids across
different subjects that leads to the reported correlations.

The IV (disturbance to the controlled variable) is the size of the SS#,
which differs across individuals. If some subjects are controlling for
bid/SS# at about the same reference, then the bids will be higher, on
average, for Ss with high SS#s compared to those with low SS#s, which
is exactly what is seen in the data.

Yes. That works. However, the form of the curves you get with this
model don’t fit the data curves. I synthesized the same data set with
the same slopes and averages for each object, using your model with the
reference slopes shown above, and got this graph to compare with the
real data graph (using the same transformations for both). Real data on
the left, synthetic on the right. The synthetic data are bowed in the
opposite direction to the real data, which seem to have something of a
slight S-curve along with the bow.

As Bill P.
has pointed out many times, it’s quite possible that the correlation
for each single subject might be in the opposite sense.

That’ seems unlikely to be the case here. But it wouldn’t matter
anyway. We are basing our thoughts about what might be controlled based
on what is observed, not on what might be observed.

Yes, I agree it’s very unlikely. But I’ve learned over the years that
if I don’t put such caveats into my messages, It is almost sure that I
will be told that I am ignoring very real possibilities.

I find it hard to look at
that plot [the left hand one above. MMT] and say that the Social
Security
number has no effect on the bid price for any subject.

I know. That’s the behavioral illusion for you. But as you know from
PCT the apparent effect of an environmental variable (SS# in this case)
on behavior (bid) is actually the control system’s resistance to a
disturbance of a controlled variable caused by the IV (SS# in this
case) and compensated for by the DV (bid).

True, but the question is what is the controlled perception, not
whether behaviour is the control of perception. The current proposals
are (a) the perception of the magnitude of a number is affected by the
prior imagining of another number (the SS#) and the controlled is the
tracking of the bid number against a perceived object value, and (b)
the perception of the magnitude of a number is unaffected by the prior
imagined SS#, and the subject is controlling not for matching the bid
to the perceived value of the object, but to a function of the
perceived value and of the SS#, the form of that function being
different for the different objects.

The plot does not seem to
suggest subjects controlled for a ratio
between SS# and bid price, because if they did, the curve would have
quite a different shape. The 0-20 bid price should be 1/3 of the 20-40
bid price (0.48 log units instead of about 1.3), whereas the 60-80 bid
price should be 7/9 of the 80-99 bid price (0.11 log units instead of
about 2.0).

I don’t understand on what basis this prediction is made.

It’s following your model, that there should be a constant ratio
between bid and SS#. Above, I modified your model to fit the data
better, by not using the ratio by itself, but by adding a constant to
give the best linear fit to the data. But what I said that you don’t
understand is what you yourself proposed.

I can predict these data quite well under the assumption that
subjects are controlling the bid/SS# ratio at about the same reference.

But you didn’t, because if you had, you would have seen that the fit
for some of the objects is not too good. Compare this new figure with
the left figure above. It’s what you get if you fix the slope (the
“ratio”) to the same value for all the objects, at the average of all
the slopes.

The exact shape of the curves is bound to be a little bumpy,
since what is plotted are averages and not all subjects will be
controlling this relationship and those who are will not be controlling
it at the same reference level. But if there are at least some bid/SS#
controllers in each group controlling relative to about the same
reference you will see a monotonic increase in the curves for each
product.

If thinking about the SS# does affect the reference value for the bid
perception, it must do so by some way other than as a simple ratio.
What might the mechanism be? And what the function?

I’m not saying that SS# affects the reference for bid perception. I’m
saying (hypothesizing, really) that the controlled variable is bid/SS#
= k; k is the controlled variable; variations in SS# are a disturbance
to that variable. The reference for that variable is unknown, but it
looks like it’s about .2 or so.

Overall, I don’t think the ratio model predicts the data very well,
even in my revised “linear slope” form.

Before you say that I haven’t made numerical predictions for the
“altering perception” proposal, I acknowledge the fact. That is because
this proposal suggests that the SS# has some effect that is as yet
unspecified on the perceived magnitude of the bid numbers. Since the
data curves pretty well overlay each other after transforming to
logarithms and subtracting the average, one might assert that this
effect is at least in part on the scale of the number magnitude
perception. However, because this is working backward from the data, it
is not legitimate to use it to fit the data. Either there has to be
some independent way of determining the form of the effect, or one has
to use these data to find the form of the effect and then do a
different experiment to see if the new data can be fitted using this
form.

Really, I don’t think we can say at this point that either proposal is
well supported by the data, the “bid/SS#=k” proposal because it doesn’t
fit the data, and the “altered perception” proposal because its form
would need to be fitted by reference to the data it is supposed to
explain, meaning that a data-fit test would not be legitimate.

Martin

···

Bill_Powers1 · November 11, 2009, 5:20pm

[From Bill Powers (2009.11.11.0845 MDT)]

Martin Taylor 2009.11.10.23.48 –

Rick Marken (2009.11.10.1320)

···

–

Martin Taylor
(2009.11.10.12.06)–

Rick Marken (2009.11.10.0740)–
Rick: My theory is that the apparent effect of SS# on bids
results from the fact that subjects are controlling for something like a
perception of the ratio bid/SS# = k.
Martin: Is there something in the reported data that would lead you
to guess that any subject is controlling for a relationship of any kind
between the SS# and the bid?

Rick: Sure. The fact that the bid increases with SS# suggests that
subjects are controlling a relationship between the bid and
SS#.

I would have to ask what happened to Rick’s repeated warnings about the
behavioral illusion. As far as I know, the only way to see whether a
subject is controlling for the average ratio of SS# to bid is to disturb
the ratio and see if the ratio is restored to its former value by a
change in the subject’s behavior. I don’t see offhand how that could be
done, so this effect remains an Unexplained Behavioral Phenomenon, or
UBP. That’s the psychological equivalent of a UFO. Is a UBP report
something important that should be investigated further, or is it, like
many UFO reports, simply an ordinary phenomenon seen under unusual
conditions? Since answering even that question often requires a
substantial investment of time and resources, there has to be some pretty
convincing evidence from the beginning to justify any further pursuit of
the UBP.

I once drove 200 miles to downstate Illinois and spent a day and a half
to investigate (for Allen Hynek and Project Bluebook) a dramatic report
of a low-flying UFO that roared past a sheriff’s deputy at night,
flashing its lights and making a screaming noise, on the outskirts of
town. At one point during the interview, I asked the officer if he had
any explanation for what he saw. He said, as I recall, “Well, it
could have been a train – the tracks run right by that place up on an
embankment” In fact, now that I mentioned it, he decided it probably
was a train. In fact, a freight-train pulled by a diesel locomotive
usually went over the bridge at the time the observation was made, he
said – he’d forgotten about that. The fog, the officer added, probably
made the appearance of the locomotive’s oscillating headlight somewhat
strange. Fog? Nobody had mentioned that unusual condition, or the
oscillating light, or the elevated railroad tracks (on a curve, he
added), up to then. All very matter-of-fact, no apology for sending me on
a wild-goose chase. The officer didn’t seem at all embarrassed.

Most UBPs, I think, are the result of testing variables that are hard to
evaluate or not of much importance to the subject. They are almost
uncontrolled. Very small mutual disturbances will have large apparent
effects because of the low or absent loop gains. Unlike the way more
important variables are controlled, the variables observed in connection
with unimportant UBPs can be influenced by almost any other variable with
any sort of connection to them, with little if any resistance. The
influence might be perfectly real, due perhaps to a slight amount of
crosstalk between neurons as I suggested yesterday, but of no importance
to the subject because what is being disturbed is not a controlled
variable, or not one that will be stabilized with any insistence.
Variables that are really under control are hard to disturb.

Best,

Bill P.

P.S. Maybe after each experimental run is done, the experimenter could
tell the subject that he wanted to read back the bids to see if he had
recorded them correctly. On the readback, he would change the bid numbers
up or down by various amounts and see if the subect objected to them or
corrected them. Goldstein and Robertson used something like this approach
to test for control of self-image.

rsmarken · November 11, 2009, 5:22pm

[From Rick Marken (2009.11.11.0920)]

Martin Taylor (2009.11.10.23.48)_-

Rick Marken (2009.11.10.1320)

The reference ratio of bid/SS# is .2. My SS# (last 2 digits)
is .55. If I bid 11 the perceived ratio of bid/SS# will be at the
reference.

Two questions.

Where does this reference ratio come from.

Higher order control systems.

What is it about the different objects that disturbs this putative
higher level controlled perception to change that reference value?

I think what is controlled at the higher level must be something like the relationship between the object and the price.

On
the assumption that the reference value averaged across subjects for a
specific object was fitted by value = k*SS# + constant, I get the
following values for k:

Trackball 0.2222

Keyboard 0.43415

Book 0.18725

Chocolate 0.12405

1998 Wine 0.1977

1996 Wine 0.2687

Nice. Makes some sense.

Those reference values for k range over a factor of about 3.5, so there
must be something about the specific objects that disturbs some
higher-level controlled perception in such a way that its output to the
reference input of the bid/SS# ratio control system varies over this
wide range. What about the objects might be perceived to produce that
disturbance?

I think we just learn from experience what references to set for the relationship between the objects and what they cost.

Yes. That works. However, the form of the curves you get with this
model don’t fit the data curves. I synthesized the same data set with
the same slopes and averages for each object, using your model with the
reference slopes shown above, and got this graph to compare with the
real data graph (using the same transformations for both). Real data on
the left, synthetic on the right. The synthetic data are bowed in the
opposite direction to the real data, which seem to have something of a
slight S-curve along with the bow.

Good job. Though the fit looks pretty good to me, especially considering the fact that the “real” data points are based on averages.That “bump” you see for the level 2 SS#s, for example, may result from the fact that you have one or two subjects in that group who had a particularly high reference for the bid/SS# ratio (if that’s what they were controlling for) or who just ignored the SS# and came up with higher bids. You really can’t use average data like this to test for the variables that individuals control.

True, but the question is what is the controlled perception, not
whether behaviour is the control of perception.

You betcha! (And there is no “u” in “behavior”

The current proposals
are (a) the perception of the magnitude of a number is affected by the
prior imagining of another number (the SS#) and the controlled [variable] is the
tracking of the bid number against a perceived object value, and (b)
the perception of the magnitude of a number is unaffected by the prior
imagined SS#, and the subject is controlling not for matching the bid
to the perceived value of the object, but to a function of the
perceived value and of the SS#, the form of that function being
different for the different objects.

These are not quite what I would call descriptions of possible controlled variables. One possible controlled variable (the one I suggested) is: CV= bid/SS#. Another, suggested by Bill, is: CV = f(SS#,Bid). The function was not specified; Bill just suggested that the perception of SS# and bid may be non-orthogonal, so the f() just indicates that these perceptual variables are combined in some way to produce the variable that is actually controlled. I think your proposal, which is that the SS# makes the bid seem smaller, could be written as: CV = k1bid - k2SS#.

I can predict these data quite well under the assumption that
subjects are controlling the bid/SS# ratio at about the same reference.

But you didn’t, because if you had, you would have seen that the fit
for some of the objects is not too good. Compare this new figure with
the left figure above. It’s what you get if you fix the slope (the
“ratio”) to the same value for all the objects, at the average of all
the slopes.

Again, I think the fit depends strongly on the fact that the data points represent averages over subjects who are likely to be controlling for different variables or the same variables at different references. All the data show is that, on the average, there seems to be a tendency to be influenced in one’s bids by SS#, suggesting that most subjects incorporate SS# in some way into the perception they are controlling with their bid.

Really, I don’t think we can say at this point that either proposal is
well supported by the data, the “bid/SS#=k” proposal because it doesn’t
fit the data, and the “altered perception” proposal because its form
would need to be fitted by reference to the data it is supposed to
explain, meaning that a data-fit test would not be legitimate.

I think your “altered perception” proposal is very similar to my bid/SS# proposal. In both cases, the SS# is a disturbance to a perception that includes both the bid and SS#; It is that perception – call it “value” perhaps – that is being controlled by the subject. Controlled perceptions are perceptions that are functions of both environmental events (disturbances), such as the SS#, and behavioral outputs, such as the bid. When you think of it that way – rather than as the SS# having an effect on the bid perception – then you have a better idea of the controlling that’s going on in this experiment, I think.

Best

Rick

···

–
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

rsmarken · November 11, 2009, 7:14pm

[From Rick Marken (2009.11.11.1115)]

Bill Powers (2009.11.11.0845 MDT)–

Rick Marken (2009.11.10.1320)

Rick: Sure. The fact that the bid increases with SS# suggests that
subjects are controlling a relationship between the bid and
SS#.

I would have to ask what happened to Rick’s repeated warnings about the
behavioral illusion. As far as I know, the only way to see whether a
subject is controlling for the average ratio of SS# to bid is to disturb
the ratio and see if the ratio is restored to its former value by a
change in the subject’s behavior.

Yes. All I was saying is that the data “suggest” that this ratio might be what is controlled by some subjects (the Ariely data is averages so the “suggestion” of what is controlled is very hypothetical with respect to an individual). That suggestion would be the starting hypothesis in a test of the controlled variable, which would involve testing one subject at a time by applying disturbances to this variable to see if they are resisted.

I think what’s useful about discussing this experiment is that shows how conventional behavioral experiments rely on subjects acting purposefully, even if we don’t know exactly what their purposes (controlled variables). The Aierly experiment takes for granted that the subjects can carry out the purpose of assigning bid values to goods. The experimenter’s goal is to see if the purposefully produced result (bid), which is viewed as a generated output (DV) is influenced by things like putting the subject’s SS# (last 2 digits) next to where the bid will be written. If there is a relationship between SS# and bid it is seen as the SS# causing the bid becuase the bid is still seen as a generated output. But we see the SS#-bid relationship as an indication that the sbujects are carrying out a purpose (controlling a variable) to which SS# is a disturbance that is compensated for by the bid. Purpose is there in all conventional experiments or nothing would happen at all.

Best

Rick

···

–
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

MartinT · November 11, 2009, 8:19pm

[Martin Taylor 2009.11.11.13.46]

To Bill Powers [From Bill Powers (2009.11.11.0845 MDT)]

BP: I would have to ask what happened to Rick’s repeated warnings about
the
behavioral illusion. As far as I know, the only way to see whether a
subject is controlling for the average ratio of SS# to bid is to
disturb
the ratio and see if the ratio is restored to its former value by a
change in the subject’s behavior.

MT: (I note that my spell checker complains about the missing “u” in
behaviour Rick considers that the SS# should be taken as a
disturbance to that ratio, in which case, perfect control would bring
the ratio to the same value for each bid made by a given subject. I
agree with him. We can use these data in “The Test” to see whether that
is indeed the case, provided that the subjects with different SS
numbers can reasonably be assumed to control with a similar range of
reference ratios. The fact that these data are based on subject groups
rather than individuals does make the analysis problematic, but we work
with what we have.

My suggestion also implies the use of “The Test”, taking SS# as a
disturbance to a controlled variable. It proposes that the controlled
variable is not that ratio, but the perceived value reported for the
bid, and that the SS# disturbs the perception of the value
corresponding a number in some way. Below, I will report the results of
testing the assumption that this “some way” is a pure scaling, meaning
that the SS# multiplies the apparent value of all bid numbers by a
constant for a particular subject. As does Rick’s, this suggestion
treats the variation of the SS# as a disturbance to the proposed
controlled variable, and the analysis asks how well the subjects are
controlling if indeed the proposed controlled perception is the correct
one.

No, it’s not a tracking study, I’m afraid.

[From Rick Marken (2009.11.11.0920)]

Martin Taylor
(2009.11.10.23.48)_-

Rick Marken (2009.11.10.1320)

The reference ratio of bid/SS# is .2. My SS# (last 2 digits)
is .55. If I bid 11 the perceived ratio of bid/SS# will be at the
reference.

Two questions.

Where does this reference ratio come from.

Higher order control systems.

What might a higher control system be controlling for that requires a
particular value of a bid/SS# ratio in order to bring its controlled
perception near its reference value?

What is it about the different objects that disturbs this putative
higher level controlled perception to change that reference value?

I think what is controlled at the higher level must be something like
the relationship between the object and the price.

Somehow I don’t see in that answer what it is that makes the
relationship for keyboards so different from the relationship for
chocolate. What difference between keyboards and chocolate disturbs
whatever perception that is controlled at this higher level? In other
words, what is that perception whose output function alters the
reference for the bib/SS# ratio, and why is it so differently disturbed
by chocolate as compared to a keyboard?

On
the assumption that the reference value averaged across subjects for a
specific object was fitted by value = k*SS# + constant, I get the
following values for k:

Trackball 0.2222

Keyboard 0.43415

Book 0.18725

Chocolate 0.12405

1998 Wine 0.1977

1996 Wine 0.2687

Nice. Makes some sense.

Those reference values for k range over a factor of about 3.5, so there
must be something about the specific objects that disturbs some
higher-level controlled perception in such a way that its output to the
reference input of the bid/SS# ratio control system varies over this
wide range. What about the objects might be perceived to produce that
disturbance?

I think we just learn from experience what references to set for the
relationship between the objects and what they cost.

That’s not answering the question, either. We aren’t asking about the
relationship between objects and what they cost, but about the
relationship between bid price and SS#, which is not something of which
we have any prior experience. Specifically, I asked what perception is
disturbed by a property of the objects, that is brought back to its
reference value by altering the reference value for the relationship
between objects and the bid price.

…

Again, I think the fit depends strongly on the fact that the data
points represent averages over subjects who are likely to be
controlling for different variables or the same variables at different
references. All the data show is that, on the average, there seems to
be a tendency to be influenced in one’s bids by SS#, suggesting that
most subjects incorporate SS# in some way into the perception they are
controlling with their bid.

Yes.

Really, I don’t think we can say at this point
that either proposal is
well supported by the data, the “bid/SS#=k” proposal because it doesn’t
fit the data, and the “altered perception” proposal because its form
would need to be fitted by reference to the data it is supposed to
explain, meaning that a data-fit test would not be legitimate.

I think your “altered perception” proposal is very similar to my
bid/SS# proposal. In both cases, the SS# is a disturbance to a
perception that includes both the bid and SS#; It is that perception –
call it “value” perhaps – that is being controlled by the subject.
Controlled perceptions are perceptions that are functions of both
environmental events (disturbances), such as the SS#, and behavioral
outputs, such as the bid. When you think of it that way – rather than
as the SS# having an effect on the bid perception – then you have a
better idea of the controlling that’s going on in this experiment, I
think.

Yes. The difference between the proposals is that the altered
perception proposal considers that there’s no relation between the bid
and the SS#, but there is a relation between the SS# and the perception
of the magnitude of the number that is used for the bid. Both proposals
consider the SS# to be a disturbance to a putative controlled variable,
so to test between them we really ought to use the same technique as
you used in comparing different putative controlled variables when a
rectangle is being controlled to stay the same size (if I remember
correctly). The following is an attempt to do just that.

I did say yesterday that it would not be legitimate to use the data to
specify the parameters of the test, but then I realized that this is
what we always do when fitting curves, and it’s OK provided the fits
don’t use too many of the data degrees of freedom. So I went ahead and
made an Excel model for the “altered perception” proposal, namely that
the imagination of the SS# simply multiplies the scale of the numbers
when they are used to represent value. In other words, after imagining
SS# X, the subject scales all the subsequent numbers by x, so that an
object for which an appropriate value is, say, $10 would be given a bid
of $10*x. The data suggests this as a reasonable possibility, because
when they are plotted logarithmically the plots for the six different
objects form pretty good parallel curves (as I showed in my previous
two messages).

So, for each of the five SS# bands individually, I generated a scaling
factor by averaging the differences of the log bids for each object
from the overall average log bid for that object across SS# bands, and
then exponentiating this average difference. I then divided each of the
bids by the resulting ratio to create a synthetic (predicted) bid. If
scaling is the correct influence of the SS# on the perception of the
value corresponding to that number, and perceived value is the
controlled variable, then the scaled bids for any one object should all
be identical across SS# bands. Every scaled bid should be the same as
the average scaled bid for that object. This approach uses 5 df from
the data to estimate the other 25.

To test this Altered Perception (AP) quasi-model against the
“Bid-Ratio” (BR) quasi-model, I estimated what the bids would have been
if control against the SS# disturbance were perfect under either model.
To recapitulate what I did for the BR model, I fitted a straight line
through the data points for each object and estimated a slope and
average for each. Perfect control under this proposal would yield
points exactly on this line, so those points became the predicted
(synthetic) bids. This approach uses 10 df to estimate the other 20.

To test the degree of control implied by each proposal, I took the
ratio between the predicted and actual bids for all 30 data points, and
subtracted 1.0 (since with perfect control the ratio would be exactly
1.0). The standard deviations of these residual error ratios were .152
for BR and 0.097 for AP. Interestingly, although neither explicitly
uses the average values over objects at any stage in the analysis,
there is a big difference in how well the two proposals fit those
averages. This figure shows the deviation of the average residual error
ratios across objects for the different SS# bands under the two
proposals.

When I made my initial interjection into this thread, I wanted only to
suggest a possibility different from those that had been proposed, all
of which involved altering the reference value for some controlled
perception, as a consequence of a disturbance to another. I wanted to
suggest that there might be no alteration in the reference value for
any controlled perception when the SS# disturbance was introduced, but
that instead maybe the perception that was being controlled was altered
by the disturbance. I had not expected that such a simple effect as a
pure scaling of the perceived magnitude of the number used to match the
perceived value of an object might suffice to explain so much of the
data. Even yesterday I did not expect that, but the parallelism of the
log bid values for the different objects led me to try it. The results,
especially the result shown in this figure, surprised me greatly.

None of this proves that the controlled variable is indeed the
perceived magnitude of the number to be equated with the object’s
value, but it does say that if subjects are controlling either of the
two proposed perceptual variables in the way proposed, and if the
behaviour of group averages can in this case be taken as representative
of any single subject, then the “Altered Perception” proposal should be
preferred to the “Bid Ratio” proposal on three grounds:

AP uses fewer degrees of freedom in its explanation by a factor of
2,
AP fits better by a ratio of about 3/2 (meaning that the fit per
degree of freedom used is about 3 times better), and
the AP average residual error fits are very much smaller are not
affected by the SS# range.

I’m afraid this has been too much fun and taking more of my time than
I had intended to spend away from what I ought to be doing. So I will
probably retire again for a while except for possible short intrusions.

Martin

rsmarken · November 11, 2009, 9:29pm

[From Rick Marken (2009.11.11.1330)]

Martin Taylor (2009.11.11.13.46) –

Yes. The difference between the proposals is that the altered
perception proposal considers that there’s no relation between the bid
and the SS#, but there is a relation between the SS# and the perception
of the magnitude of the number that is used for the bid

What is the CV in your altered perception (AP) model?

Both proposals
consider the SS# to be a disturbance to a putative controlled variable,
so to test between them we really ought to use the same technique as
you used in comparing different putative controlled variables when a
rectangle is being controlled to stay the same size (if I remember
correctly). The following is an attempt to do just that.

Great. But in that test I had a definition of both possible controlled variables. I know that the controlled variable in the bid ration (BR) model is bid/SS#. What’s the controlled variable in the AP model?

To test this Altered Perception (AP) quasi-model against the
“Bid-Ratio” (BR) quasi-model, I estimated what the bids would have been
if control against the SS# disturbance were perfect under either model.

To do that you would have to know what controlled variable SS# is a disturbance to. What was the controlled variable in the AP model?

AP uses fewer degrees of freedom in its explanation by a factor of
2,

AP fits better by a ratio of about 3/2 (meaning that the fit per
degree of freedom used is about 3 times better), and

the AP average residual error fits are very much smaller are not
affected by the SS# range.

Great. But what is the CV in the AP model?

Maybe you could send me the spreadsheet so I could see what you did?

Best

Rick

···

–
Richard S. Marken PhD
rsmarken@gmail.com

www.mindreadings.com

Bill_Powers1 · November 11, 2009, 9:55pm

[From Bill Powers (2009.11.11.1424 MDT)]

Martin Taylor 2009.11.11.13.46 –

MT: To test the degree of
control implied by each proposal, I took the ratio between the predicted
and actual bids for all 30 data points, and subtracted 1.0 (since with
perfect control the ratio would be exactly 1.0). The standard deviations
of these residual error ratios were .152 for BR and 0.097 for AP.
Interestingly, although neither explicitly uses the average values over
objects at any stage in the analysis, there is a big difference in how
well the two proposals fit those averages. This figure shows the
deviation of the average residual error ratios across objects for the
different SS# bands under the two proposals.

BP: My hat is off to you, Martin. This is a beautiful job of teasing a
startling regularity out of data in which it is well hidden.

MT: I wanted to suggest that
there might be no alteration in the reference value for any controlled
perception when the SS# disturbance was introduced, but that instead
maybe the perception that was being controlled was altered by the
disturbance. I had not expected that such a simple effect as a pure
scaling of the perceived magnitude of the number used to match the
perceived value of an object might suffice to explain so much of the
data.

Can you confirm that this is a scaling of the perception according to the
magnitude of the SS#, and not an additive contribution to a constant
perceptual signal? My proposal of a “leak” from one perceptual
channel into another would imply an additive effect, though if there is a
logarithmic function behind the perceptual signals an additive effect
would imply a multiplicative effect on the original magnitude. An overall
scaling of a linear representation would imply that the SS# actually
multiplies the other perceptual function by a constant – and according
to your results, remarkably constant – factor. On the other hand, if
what is controlled is the affected rather than original perceptual signal
(whatever it is), the additive interpretation might still hold up. Your
use of ratios rather than differences leaves some questions unanswered.

What’s needed here, when you find the time, is the actual control system
model, so we (meaning those sufficiently capable) can unpack all the
implications of your finding. I have a feeling that you have found
something new that is highly publishable. It should be examined very
closely, of course, before going that far.

Best,

Bill P.

MartinT · November 12, 2009, 6:05am

[Martin Taylor 2009.11.11.23.43]

[From Bill Powers (2009.11.11.1424 MDT)]

Martin Taylor 2009.11.11.13.46 –

MT: To test the degree
of
control implied by each proposal, I took the ratio between the
predicted
and actual bids for all 30 data points, and subtracted 1.0 (since with
perfect control the ratio would be exactly 1.0). The standard
deviations
of these residual error ratios were .152 for BR and 0.097 for AP.
Interestingly, although neither explicitly uses the average values over
objects at any stage in the analysis, there is a big difference in how
well the two proposals fit those averages. This figure shows the
deviation of the average residual error ratios across objects for the
different SS# bands under the two proposals.

BP: My hat is off to you, Martin. This is a beautiful job of teasing a
startling regularity out of data in which it is well hidden.

Thanks very much.

Can you confirm that this is a scaling of the perception according to
the
magnitude of the SS#, and not an additive contribution to a constant
perceptual signal? My proposal of a “leak” from one perceptual
channel into another would imply an additive effect, though if there is
a
logarithmic function behind the perceptual signals an additive effect
would imply a multiplicative effect on the original magnitude.

My guess is that this is exactly what is happening. As you and Rick
demonstrated, Stevens’ power law falls out if the perceptual magnitudes
of numbers are logarithmically related to the numeric value. If that is
true, then the effect of the SS# could easily be an additive leak.

An overall
scaling of a linear representation would imply that the SS# actually
multiplies the other perceptual function by a constant – and according
to your results, remarkably constant – factor. On the other hand, if
what is controlled is the affected rather than original perceptual
signal
(whatever it is), the additive interpretation might still hold up.

Yes, it would. To answer Rick, my proposal is that what is controlled
is indeed the affected perceptual signal – the perceived magnitude of
the number that is to be made to correspond to the perceived value of
the object. The perceived value of any given object is assumed to be
constant, analogous to the position of the target in a compensatory
tracking study. Obviously this isn’t true across individual subjects,
but averaging across subjects it may not be too far off. The data do
suggest, for example, that in the 20-40 range of SS numbers more
subjects valued wine highly than in the 40-60 band.

Under this assumption, the SS# also ought to be logarithmically
transformed before the leak, which should make the log scale factor
linearly related to the log SS#. Maybe it is, and maybe it isn’t. I
can’t tell from these data, as this figure of log scale factor versus
log SS# shows. It’s too noisy, in part perhaps because the SS numbers
would not be uniformly distributed within the SS# bands. Any
nonuniformity would shift points in the figure (especially the point
for the 0-20 band) left or right as compared to their location in the
figure, which assumes a uniform distribution.

Your
use of ratios rather than differences leaves some questions unanswered.

I used ratios because the linearity showed up only when the raw bid
data were logarithmically transformed. If you take the log data as
“raw”, then everything becomes differences.

What’s needed here, when you find the time, is the actual control
system
model, so we (meaning those sufficiently capable) can unpack all the
implications of your finding. I have a feeling that you have found
something new that is highly publishable. It should be examined very
closely, of course, before going that far.

It’s an ordinary compensatory tracking model with the object’s
perceived value as a reference level, but with a logarithmic transform
for the perceptual magnitude of the bid number (the cursor). The
spreadsheet doesn’t implement the control model as a feedback loop. It
simply says “if X is the controlled perception, the output should
produce these data”, sidestepping the actual process of control. I just
ran it for X = c + kbid/SS# with c and k optimized for each object
separately, and for X = vscale, with v being the average across
subjects for each object individually and scale estimated for each SS#
band (meaning I was wrong to say this proposal used only 5 df in the
data fit; it actually uses 10df, the same as for the bid-ratio
proposal).

Martin