Toward an Informational Dynamics of Collective Choice

Toward an Informational Dynamics of Collective ChoiceAuthor(s): Pam BrownSource: Public Choice, Vol. 39, No. 3 (1982), pp. 415-420Published by: SpringerStable URL: http://www.jstor.org/stable/30023633 .

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Why so much stability?

Toward an informational dynamics of collective choice

PAM BROWN

Abstract

In the following argument, it is suggested that the informational dimension of small-scale collective choice systems be introduced into the set of explanatory variables, be allowed to fluctuate while the 'committee' is in session and, finally, be permitted to "feed back" to the individual participants during the group decision process. It is suggested that consideration of the

in-period or 'in-committee' shocks which this release and flow of information may be modeled to have on the participants' round-to-round voting strategies might provide a supplementary explanation of some of the anomalous results (such as the relative rarity of observed cycling) encountered in observations of collectively controlled systems.

Models of men in collective decision systems typically assume that individual

preference orderings generated with respect to the set of alternatives to be considered by the group remain constant during the group's decision process. These schedules are usually posited as being formulated on the basis of two factors or 'inputs': (1) the set (sequence (agenda) for as well as array of) the alternative goods or bundles from which the group will make its selection; and

(2) any information which might be available to the individual voters (through accessible past voting records, circulating survey or polling results, private conversations, etc.) concerning the probable preferences of the other members of the impending congregation.

What is common to most existing models, usually found to incorporate an informational assumption which ranges from "perfect foresight" to complete "myopia", is the (implicit or explicit) restriction that the individual's voting strategy, whether "naive" or "sophisticated", is completely determined and, for the duration of the analysis fixed, at the start of the collective decision

process or period. The domain of collective control is assumed to be charac- terized by information "impactedness"; no mechanisms are included in the scenarios which might allow for the possibility of in-committee or 'in-period' strategy revisions in the face of new or additional information on the group's

* Center for Study of Public Choice, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061.

Public Choice 39: 415-420 (1982) 0048-5829/82/0393-0415$00.60. ( 1982 Martinus NijhoffPublishers, The Hague. Printed in the Netherlands.



416

or its members' preferences - data which will in most situations necessarily tend to be generated as a by-product of the collective decision process.

Of course, there appear to exist cases in which such a restriction makes an important contribution to the realism of the model. There seem, however, to be numerous other instances in which such an imposed limitation is inap- plicable; and if one does not want to say that the individual decisionmakers experience a discontinuous jump from being rationally economizing information-retrievers outside the group setting to unadaptive agents which fail to take advantage of exploitable new data inside, then the restriction is perhaps best dropped or modified, and a revised model opted for.

By incorporating a strategy revision rule conditional upon changes in the amounts of information available in the system at each point in the voting sequence, actual voters in information-fluid situations may be modeled with the capacity to search for, learn from, and make strategic adjustments by taking account of continuously shifting supplies of knowledge. To produce what can be described as a powerful (i.e., restrictive) model of the potential impact of this informational feedback, limitations must be placed on (1) the nature of the information to which the individual voters are allowed to have access during the meeting (i.e., its availability or costliness, "quantity" (however this might be measured), "quality" (or conversely, the amount of "noise" in the system), direct usability (the degree to which the informational signal or message might be encoded and may therefore require a transformation of some kind before it can be used in strategy (re-)design)); and (2) the adaptive or learning responses of the participants, as these are expressed through changes or revisions in the members' voting strategies or expressed preferences. In short, we need to place limits on the information flux occurring within the collective, and strictly specify an in-period or in-committee strategy "trajec- tory" for each individual participant in the group decision system.

What might the results look like if we were to permit such in-committee adaptation to take place? An idea of how radically different the predicted results of a given collective process can be when in-process strategy revisions are permitted is shown by the following simple example.

Consider the following elementary 3-by-3 majority-rule model, in which each of the three voters 1, 2 and 3 is assumed to be interested in obtaining his most preferred of the three alternative options a, b and c:

Table 1.

Individual: 1 2 3

a b c

Preferences: b c a

c a b



417

If we assume, as is standard, that the individuals' voting strategies are "fixed" (constant) throughout the sequence of votes on all possible pair-wise comparisons (we allow here no explicit agenda control), then, assuming that the individual voters make decisions as part of the group solely by reference to their ("true") schedules as given above, the result is the following familiar cycling of outcomes:

aPbPcPaPb---.

Now consider the consequences of permitting voters the opportunity of making in-period or in-process strategy revisions on the basis of informational feedback, where the results of each pairwise comparison in the sequence considered by the committee represent the new data received. As noted above, if determinate results are to be obtained, some specific assumption(s) about the manner in which this adaptive process takes place must first be outlined. Let us assume that (1) the three voters are completely ignorant of (or alter- natively, are completely "suspicious" of the reliability of any apriori-obtained information on) the true preferences of the other group members, initially; (2) any in-committee information received by voters concerns collectively- determined outcomes only (i.e., individual ballots remain private); (3) following convention, all three participants adopt a "naive" voting strategy (i.e., the voters' "true" preferences are also given as their in-committee "strategically" expressed preferences), in light of their assumed initial ignorance, for use in the first round of voting; (4) each voter uses an "avoid-the-worst" (see Plott and Levine, 1978) algorithm for strategy revision; and (5) the (arbitrarily selected) sequence in which the three alteratives are to be exhaustively pair-wise compared will be a versus b, b versus c, and a versus c. How will this revised assumption set affect the results of this simple model?

The group must first select between alternatives a and b. If we let the preferences given in Table 1 represent the voters' "true" preference schedules, then, again, assuming that the individuals' strategy-formation rules dictate that they vote according to their "true" preferences initially, the result of the vote is the selection of option a.

The information is now out that a can beat b in a committee vote. Recall that we are assuming that this is all, outside of his own preferences, that each individual now knows. Given the presence of this informational feedback, what will the voters do?

Assuming an "avoid-the-worst" strategy revision rule for the three players-voters, the following strategy changes, as they are evidenced through alterations in the voters' "in-committee" expressed preference schedules, will be introduced:



418

Table 2.

Individual: 1 2 3

a c c

Preferences: b b a

c a b

For reference in determining his strategic voting behavior in the coming (second) round, individual 2 has revised or adjusted his expressed preference schedule - as an in-process response to changes in the amount of information on the behavior of the collective - from bP2cP2a, his "true" preference ordering, to cP2bP2a. He has done this because his information set now includes the knowledge that (1) b can be beaten by a in committee vote; (2) it is possible that c, which has yet to be compared with a in committee, will beat it (a); and trivially, (3) he wants if possible to avoid a, his "worst" choice. He therefore "revises" his in-committee expressed preferences/voting strategy, and enters the next round of voting with the revised ordering given in Table 2 above.

The next pair-wise comparison is b versus c. Basing the outcome on the second, informationally adjusted, set of ordering relations, c wins a majority of votes for this round.

The last (third) pair of options to be considered by the committee consists of a and c. It will be noted that in this case, these two alternatives will be ranked by the three members according to the expressed preference orderings given in Table 2 again. No changes in the strategies of the voters will have occurred following the second round, because, given the information from the first two votes along with the "avoid-the-worst" strategy revision rule posited earlier, it can be seen that no further adjustments can be made in the expressed preferences/strategies of any of the three voters-players which will serve to improve their present positions. None of the voters has anything to gain from engineering a revision in the voting strategy which he has incorporated into his expressed preference schedule following the feedback from the first round of voting. Since there exists only one more pair of options to consider, we could characterize the individuals as at this point in the political process having reached their informational saturation points; and the system as a whole, as having attained an informational equilibrium with respect to its release of usable information concerning the collective "black box".

The voting equilibrium, however, has yet to be determined. It is obvious that the result of an a-versus-c comparison, based upon the preference orderings given in Table 2, is cPa. The collective preference schedule which results from the introduction of in-period 'informational dynamics', then, is

cPaPb,



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a determinate, transitive, ordering of the three alternatives. The (unique) group choice in this case would of course be c.

Decision and search are both integral aspects of economic and political behavior. Models of man which are interested in exploring both of these problems might find it productive to investigate more sophisticated models of 'homo economicus' and politicus, depicting the human agent as a machina docilis as well as a machina judicatrix.

Assuming away knowledge problems by positing either "perfect" foresight in an informationally "complete" world, or, fixed, "myopic" strategy- and expectations-formation mechanisms in a world of in-period informational impactedness is an approach which eliminates the messier aspects of the analysis, along with some of the possibly more useful ones.

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Toward an Informational Dynamics of Collective Choice