Political equality in a large group

October 29, 2009

This post is aimed at being the first part in a long-delayed “attempt to embark on” “a methodical analysis of the set of possibilities for achieving political equality”.

Part 1: Optimal decision-making, group rationality

… in which it is argued that groups, in an ideal setting, can achieve rational decisions. Group decision making constrained by practical circumstances should therefore be designed so as to produce decisions that approximate the decisions that would have been made under ideal conditions.

It is sometimes asserted that groups cannot form good policy. When such notions are expressed by the less educated, they are are attributed to the authoritarian sentiments of the unsophisticated. When such ideas are proposed by the educated, they are considered evidence of hard-headed realism. Elite speakers often mention Arrow’s “impossibility theorem” (what Arrow called the ‘General Possibility Theorem’) and claim that it “shows” that group rationality is impossible.

It is regularly observed that such claims are greatly overblown (e.g., chapter 2 of Majid Behrouzi’s Democracy as the Political Empowerment of the Citizen) – that the theorem is based on a very specific conception of group decision making whose validity and relevance are very circumscribed. In particular, it is based on the notion of “the individual” within the group as an atomic rational entity, who arrives at its decisions (or preferences) rationally. In fact, it is quite natural to see an individual as an entity that has to balance multiple, often conflicting, preferences. Thus, the individual is performing the same task that the group decision making mechanism is supposed to be performing. If the group cannot act rationally, neither can the individual.

The criterion for the feasibility of rationality cannot, therefore, be individual vs. group. It seems that the appropriate measure of the feasibility of rationality in decision making is the availability of time and motivation to investigate the circumstances and considerations that are relevant to the decision and to act in accordance with the findings. When a single person is involved, those circumstances and considerations are those of that person. When a group is involved they are of all the members of the group. A hurried or uncaring person would arrive at a decision that is much inferior to that of a group that has the leisure and motivation to optimize its decision, for a rational decision requires allocation of appropriate time, resources and effort.

Under ideal conditions, a person, or a group, as large as it may be, can consider a situation and arrive at the appropriate – rational, optimal – decisions. Such conditions would include the time and motivation to assimilate all the relevant information, to consider all the relevant interests, suggest all the feasible alternatives and arrive at a decision. Under such conditions, the decision maker (a person or a group) is not constrained by any pre-existing rules (since these may be changed by the decision making process), while deadlocks and cyclic preferences pose no more of a problem for a group than they do for the individual.

In addition, under ideal conditions, political equality can be introduced by simply adding a requirement of symmetry among all the members of the group, since under ideal conditions there would be no significant barriers to the existence such a symmetry.

The problem of decision-making under realistic conditions is therefore that of approximating decision making under ideal conditions. It is a problem of allocating power and resources and inducing motivation in such a way as to produce decisions that are as close as possible to those that would be the result of decision making under ideal conditions. This problem is not trivial under a wide variety of circumstances, but it grows more acute when decisions are to be made for and by a large group of people, since the ideal conditions become more and more unrealistic as the size of the group grows.

The problem of democratic decision making in a large group under practical conditions is that of approximating the decisions that would be taken by a large group of political equals under ideal conditions. It is interesting to note that since the quality of the approximation is measured in terms of the fidelity of its decisions rather than the fidelity of its process, no assumptions about political equality are built into the form of the approximating practical democratic decision making mechanism. It is conceivable that a mechanism (such as an elections based system) that involves certain political inequalities would yield decisions that better approximate the ideal democratic decision-making mechanism than would any practical mechanism that introduces no such inequalities (e.g., some form of a pure referenda-based system).

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3 Responses to “Political equality in a large group”

  1. Harald Korneliussen Says:

    I’m looking forward to this series. Your pure stats posts lately have been tantalizingly interesting, but rather short on conclusions – and I’m wary of trying to draw them myself, since I know just enough statistics to know that I should be.

    I’ve also many times been annoyed with those who use the Arrow theorem as an excuse for poor decision-making. For whatever outcome we are seeking, no matter how complex, if we can define it and measure it at all, then some decision-making systems _will_ perform better than others.

    Something I wonder about, is how much this has been studied. What I really want social choice researchers to provide me, is a table.

    Then, for any given decision, I could just look up: How many people are there in the group that should take the decision? Are their payoffs perfectly aligned (like when the group is, say, a team of chess masters trying to figure out the best move against a supercomputer), completely independent (like budget negotiations in a state so corrupt that no one benefited from what the other departements did) or somewhere in between? Do we want a system that maximises the sum of payoffs, or one that maximises the payoff for the one who gets least?

    Then it would just tell me: “Well, we did that experiment with the chess masters, and it turned out this decision procedure performed best. The theoretical justification for this is … blah blah”.

    Now, we would probably still disagree which game modeled reality better in a given situation, but at least we could agree that for this and that game, this decision procedure works best.

    [edited to removed extra line-breaks – yg]

  2. Harald Korneliussen Says:

    Sorry about the line breaks.

  3. Sortition Says:

    Hi Harald,

    How are you doing?

    Laying out my intended “methodical analysis” may take some time – it is a work in progress. I fear that the table that you suggested (i.e., if I understand you correctly, a taxonomy of decision-making situations, with the optimal decision-making system associated with each) is far out of my reach (and, it seems, out of the reach of game theorists). My hope (ambitious enough) is to create a model of decision making systems that provides a framework for analysis of the various practiced or suggested government devices (elections, sortition, referenda, expert-based decision making bodies, hierarchical delegation, etc.) and would also facilitate the discovery of other devices – hopefully, allowing a complete enumeration of all possible devices.

    In some way, this would be an elaboration of Aristotle’s classical taxonomy of governments. This kind of analysis seems to have been abandoned (or at least, drastically de-emphasized) by modern political scientists – for reasons that would be interesting to consider, perhaps.

    As for the data-only posts, please do feel free to draw your conclusions and respond. My intention is to present data that I think is relevant to topics that are of public interest. I think that technical statistical expertise is not a pre-requisite for the interpretation of such data – as opposed to common sense, and due humility (with the case of Steven Levitt being instructive on this matter).

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