Social Choice and Chance in an Open Society

By Sander Rubin

About five years ago, I made the suggestion that Mensa would best serve humanity by dedicating itself to internal political reform for an initial period of about five years [International Journal, Mar. '95, p. 1]. That is, Mensa can both do well for itself and for the larger world by acting as an experimental microcosm. Now it's time to get down to specifics.

The Open Society.

Mensa purports to be an “open society” (to use Sir Karl R. Popper's phrase, more meaningful than “democracy”). The touchstone of such a society is that it operates for the benefit of its citizens, not for its elites or governors. The fact that the principal activities sponsored by Mensa are of a social nature (and, no doubt, always will be) does not diminish the attractiveness and importance of Mensa's “round table” ideology. Yet historically, Mensa has fallen far short [see political note] of embodying such ideals.

Three critical problems in open societies are: How does the group select its governors and functionaries? How does the society choose between alternative policies and procedures? How does the society create a political structure that promotes in reality the ideals of openness? The usual method is voting in elections and referenda. Yet the popular cynicism about such political processes, the belief that sub rosa games make a mockery of the formal rules, testifies to the demoralization of politics. Can we revise the formal rules in a way that will diminish this cynicism, not merely in perception but in reality?

The Objective Problem.

It is important to understand that there is an objective basis, quite apart from corruption, for the failure of election procedures to produce results that people find acceptable. Some 40 years ago, Kenneth J. Arrow (since become a Nobel laureate) published an article in Economica outlining the impossibility of creating a voting system that will satisfy reasonable notions of fairness for all conditions of choice. Arrow elaborated his work in Social Choice and Individual Values, Wiley, 1963, and an article by Blair and Pollak in Scientific American, Aug. '83 provides a concise, if highly mathematical, summary.

The kind of anomaly that inspires cynicism can be illustrated by three examples. Some election procedures are the equivalent of running separate races between pairs of candidates. In some real cases, the context of the choices leads to logically inconsistent results. In pairwise elections, A may be preferred to B, B preferred to C, but C preferred to A! What then? In serial elections with runoffs (American Mensa's procedure is a variant of this) you can get a three-way situation in which there is unstable polarization. If candidates A and C are on opposite poles of the political spectrum (extremists with large followings) and candidate B is a moderate who is everyone's second choice and a good compromise, B will be defeated on the first round and one of the extremists will win. What a way to choose! Or, consider proportional representation, benignly intended to provide an effective voice for minorities. Under conventional majoritarian rules, parties (or individuals) have to form coalitions and enforce voting discipline regardless of the merits of particular issues. Thus, single-issue parties may find themselves at the fulcrum of the power balance and be able to force legislation not favored by the community. Ironically, it was under such well-intended rules of the Weimar Republic that the Nazis achieved power in 1933 and, under similar rules, a small orthodox minority wields disproportionate power in the Israeli government. Yet it would be offensive to deprive minorities of a proportionate effect on public policies.

What I suggest is that we now have the analytical and technical tools to overcome these anomalies. Within this century, we have acquired new understandings of the nature of the world that is inconsistent with the deterministic assumptions of the Newtonian age. If we give up determinism, we can actually do better than if we retain certain myths and preconceptions. It is interesting that Popper (1902-94), whose The Open Society and its Enemies defined the ideological basis for a society that respects its members, in one of his late works, a thin book entitled A World of Propensities (1990), drew a similar conclusion. We need to start with an examination of some peculiar psychological and doctrinal assumptions.

The Psychological Problem.

Here are the questionable assumptions:

1. Laws and rules change reality: Rather, rules describe reality, but only when they are well-formulated on the basis of empirical observation. Alternatively, rules may state intentions but do not bring those intentions about; only people's actions do.

2. A series of binary decisions will produce the result desired by the group: Rather, binary decisions are the basis of parliamentary procedure. The result obtained, in fact, will depend upon the nature and order of the choices presented. An insider who controls the wording and order of the choices can (and often does) engineer a result that is offensive to those who should be the deciding parties. Real choices usually involve trade-offs, compromises, and conflicting preferences even within a single individual. There are alternatives to binary choices that would have been difficult to realize in an earlier era but are easily accomplished now.

3. Decisions are permanent: Elections and referenda are often conducted as though the result established an eternal precedent. Although it is true that sometimes the result of a choice has long-term or far-reaching effects, it is also possible to craft choices that are limited by self-consciousness of our state of ignorance or respect for the rights of others to make different choices in the future. (Popper wrote approvingly of such policies, calling them “piecemeal social engineering”; the pejorative connotation of social engineering, acquired in a factional political context, should not prevent us from considering its merits objectively.) Sunset provisions in laws are a simple example.

4. “The majority rules” is a fundamental principle of “democracy”: But every totalitarian government in this century has, one way or another, been able formally to muster a majority. The touchstone of the open society is protection of the rights of minorities, not the rule of the majority. This is not a novel concept but explicitly the basis of our American Bill of Rights.

If we give up the illusions that have guided us and take a fresh look at the opportunities for change, the problem is reduced to proposing a practical mechanism for making better social choices. I propose that the key to such a mechanism is the introduction of an element of chance into the process of choosing. While chance may appear to diminish our control over our choices, I submit that the way in which laws (and candidates) play out in practice after the choice is made under our present procedures – counter-intuitively and perversely – we do not have such control now, and nothing is really being given up. Indeed, there appears to be an unwritten but operational rule that whatever a candidate promises in an election will be unfulfilled or reversed by him or her when elected, a major cause of cynicism. Similarly, how often have the unintended consequences of a law resulted in voters' regret within a few years? Suppose we recognize explicitly the chanciness of choices rather than fool ourselves into a false belief in our control over events.

How to Recognize Chance.

Here I shall lay out the first-order mechanism for improved social choice. There are further second-order adjustments, to be discussed later, that will overcome objections that may arise in special cases. For clarity and definiteness, the example will be based upon a model of policy-adoption, but, with suitable changes, a model of election of governors can use similar principles. Assume that the electoral body is a legislature or a committee.

Instead of laying out policy alternatives as a series of up-or-down binary choices, let all alternatives be laid out for consideration at the same time. In the debate on the issues, each member of the body can weigh the trade-offs among the alternatives and develop, internally, an ordering of preferences. It is not necessary, or even desirable, for the member to make absolute decisions between any pairing of the alternatives or even among the set of alternatives. All that is required is that some kind of “fuzzy” apportioning of preference be assigned by each member of the body. Some of the alternatives may be unacceptable to a member, some may be acceptable but not preferred, some may be strongly preferred.

Instead of a “one man, one vote” rule, give each member, say, 100 votes to be distributed among all alternatives, more to the preferred alternatives, less to the merely acceptable, and none to the unacceptable. The distribution is entirely up to the individual on whatever subjective basis he or she may use. Each member has equal voting weight in the aggregate. Once all votes have been cast, they can be tallied among the alternatives.

For example, if there are 12 members of the body (a small committee) and five alternatives (including “none of the above”) there would be 1200 votes to be distributed in the following fashion.

Alternatives A B C D NOTA
Votes 436 321 204 139 100

“A” does not win this race. It would not even win if it tallied to a majority of the 1200 votes. Majorities, with an exception to be noted later, don't count for anything in this method. All that A gets is a weight of 436/1200 or 0.3633, and similarly each alternative acquires a respective weight to yield a table like this:

Alternatives A B C D NOTA
Weights 0.3633 0.2675 0.1700 0.1158 0.0833
Cum Wghts 0.3633 0.6308 0.8008 0.9166 0.9999

At this point one does the equivalent of spin a roulette wheel or hold a lottery. That is, one generates a random number between 0.0000 and 0.9999. If the number falls between 0.0000 and 0.3633, A is the winner; if between 0.3634 and 0.6308, B wins, and so forth. In effect, the chance of winning is proportional to the preference weights; even a relatively unpopular alternative has a chance, albeit a diminished one, of winning.

The “none of the above” (NOTA) option may be interpreted either as a rejection of all the other choices and a continuation of the status quo or as a rejection of the act of choosing and a desire to continue the debate to be followed by another ballot. The definition of NOTA and rules for proceeding after such an outcome must be established in advance, of course. It is possible to have both interpretations on the ballot as distinct options: Status quo and continue. In a further variation of this voting scheme, voters may express the strength of their convictions, the degree of certainty in their choices, by not casting their full quota of votes. A voter who does not feel strongly about an issue might cast, say, only half the votes s/he is entitled to and thus register a partial abstention. Such modulation in the process would add to our knowledge of the will of the voters. When applied to a legislative process, such a rule would give valuable information about the convictions of a representative, useful to his constituents at reëlection time.

Avoiding Disasters

What is the incentive for a member to distribute his or her votes rather than put them all on a preferred choice? Assuming that the member can live with some subordinate choices and taking into account the risk that chance will favor an unacceptable choice, one wants not only to vote for one's preference but also against the unacceptable choice. This is where the majority enters the picture again.

Consider the chance, even a small one, of committing to an outrageous policy, starting a nuclear holocaust, for example. There are, in fact, people who favor outrageous actions, and they cannot be denied their place in an open society. But the policies they advocate cannot be allowed to prevail even by a remote chance. The principle to apply here is not majority rule but “the majority must not be offended.” Along these lines, the method called “approval voting” has been employed by such organizations as the Institute of Electrical and Electronics Engineers. Members vote for all acceptable candidates, not just one candidate. In the example we have been using, we add a provision that tallies the number of members that give any vote at all to each alternative, even a small number. By not voting at all for some of the alternatives, the member signals unacceptability. The incentive for giving any (even small) vote to acceptable alternatives is to deliver this signal. Then (and this is the modification mentioned earlier) before distributing the weights, any alternative that does not have at least some vote from a majority of the 12 members (not a majority of the 1200 votes) is excluded from the distribution.

What Advantages May We Expect?

Will this scheme make a difference? How? Here's what we might expect.

1. Shorter debates: Since a member may distribute votes among several alternatives and need not make a binary (yes/no) decision, some of the decision criteria can be vague. Uncertainty in the members' minds can be reflected in this distribution, and the arguments become less critical.

2. Fewer side deals and log-rolling: Since the final decision rests on chance and not the “drop dead” attainment of a numerical goal, no one can exercise swing-vote power. The stakes in any voting bargain are greatly diminished for any individual; all have equal stakes. Special-interest, single-issue blocs will have power proportionate to their numbers but cannot “blackmail” or hold up the whole body. Such minority groups can bargain for token votes to assure that they have a chance at the turn of the wheel, but they cannot get extreme programs adopted whole-hog.

3. Fewer extreme, unrealistic proposals: There are demagogues and ideologues who are prepared to destroy society for the sake of some pet principle, but most people (and legislators) are reasonable, cautious, and well-intentioned. The knowledge that a far-out, extreme proposal has a definite chance of being adopted under this scheme will probably inspire the sensible majority to apply pressure to the extremists to move more slowly and moderately. The fact that reckless proposals are perceived as non-starters by the majority actually encourages recklessness as a means to attract attention; given a chance for such proposals to become enacted, the majority is likely to give them earlier attention and quash them before they reach the decision point. Proposals that do rise to the final round of decision are likely to be more modest and contingent.

4. Consonance with the way the world really works: As Popper wrote, this is “a world of propensities.” We make real progress by taking small steps, piecemeal actions, and backing away if they go awry, not by grand plans or extreme actions. Non-linearities and uncertainties make the prediction of consequences a vain enterprise; the “law of unintended consequences” is not meaningless. We take chances in the hope of a reward but limit our risks. The conventional binary-choice procedures are inconsistent with a world that works in this way. Such procedures require far more certainty and knowledge than we actually have if they are not to lead us into dangerous waters. The leverage that “majority rule, binary-choice” processes give to the individual or bloc strategically placed at the fulcrum of power is much too risky to be tolerable.

Whether the scheme I have outlined here will work out as well as I have indicated is not something that need be debated abstractly. Political theory, in the end, rests on existential experience. There is no reason why we should not experiment with variations on this scheme using chance in making social decisions. We have nothing to lose but our illusions of control in an uncertain world.

Supplementary Comments & References

A recent (1998) book that sets out the philosophical basis for this work is Impossibility: The Limits of Science and the Science of Limits, by British cosmologist John D. Barrow. This book was reviewed in The Toronto Globe and Mail by Richard Lubbock, and the review is an excellent explanation of the motivations behind the plan I have outlined. It confirms the modern scientific and logical findings of indeterminacy and uncertainty deeply imbedded in the nature of the universe and of language, referring to the works of Einstein, Planck, Heisenberg, Wittgenstein, Gödel, and Arrow. The review makes explicit reference to the problems of “democracy” in such a universe.

If you have difficulty in seeing where this proposal fits into the “Big Picture”, read the archives at the The Toronto Globe & Mail website, or if it is no longer available there see a copy I have provided.

Click here to read a discussion of this paper on the Karl R Popper list server archive under the thread title When “democracy” fails? (explore the thread by following previous and next links) and other comments by e-mail.

Some other sites related to election procedures:
Proportional Representation: Center for Voting & Democracy.
Approval Voting: Boulder [Colorado] Computer Network.
The Science of Elections Editorial by S.J. Brams and D.R. Herschbach, Science, v. 92, p. 1441, 25 May 2001. [Requires subscription to Science magazine.]
Election Selection E. Klarreich, Science News Online, 2 Nov.2002 v. 162, No. 18. and a follow-up column. Among the number of proposals there, the one by Barry K. Rosen, involving conceptual “buckets” and “pails”, comes closest to my proposal and may be better in terms of simplicty and public acceptability; when you go to the site, do a search on his name.

[Return] Political note: There have been those in high places within Mensa who have impoverished the society for their private benefit and “justified” it by saying, in effect, “Well, that's human nature.” It ain't necessarily so. Altruism and dedication to service have been as much a part of human nature as have been selfishness and greed.
Spread sheet example
To Directory Page

Copyright © 1995, 1996 , 1997, 1998, 1999, 2000, 2002 by Sander Rubin
Related sites are welcome to establish a link to this page upon notifying me by e-mail. I shall be glad to reciprocate upon request.

Created: 06 Nov 95
Revised: 20 Jan 03