The Voter's Paradox

By Leon Felkins

Written 10/14/95

Revised 8/19/00

  1. Introduction
  2. "No snowflake in an avalanche ever feels responsible." -- STANISLAW LEC
    It is said that society is in a moral crisis. And, what is worse, it seems to be deteriorating at an ever increasing rate. We all agree that something needs to be done. Our politicians and preachers say we need to help each other more, we need to have "family values", we need to contribute to society and we need to have high moral standards. But there is a fundamental reason why none of this is going to happen. That reason may be a paradox for which there is no answer. This essay will serve as an introduction to this fascinating social problem which I will call the "Voter's Paradox". [1]

    A few nights ago, my wife and I were driving along one of the lesser traveled highways. We came upon a person with a broken down vehicle in obvious distress. My wife said, "Maybe we should help". But I said, "I think not - it is not worth the risk". She responded, "But what if someday you were stranded and needed some help. Wouldn't you want someone to stop?"

    Her reasoning is noble and her attitude is just exactly what our society needs. But her logic is faulty.

    It is faulty on at least two counts. First off, my wife and I personally had much to lose and little to gain by helping this person. There would likely be time and expense involved to us in getting the stranger's car going again. And, there was some risk in that we could have been harmed by the person. The only practical reward for all this was a possible future gain of being helped in a similar situation.

    And that brings us to the second fault; how is the recipient of our compassion going to spread the word to the population that the two of us are compassionate people (so that we might be rewarded someday when we need help)? Of course, it would not happen. Helping this person would have no effect on our chances of ever receiving similar help in this large anonymous society we now live in.

    That example illustrates a phenomenon that is ubiquitous to our society.

    When an individual has reason to contribute to what is basically a group activity in which the benefits of the group activity are shared by the group, certain puzzling phenomena are evident that can only be described as "diabolical". While there is no generally accepted terminology for these phenomena, various manifestations are often referred to as the "Voter's Paradox", the "Volunteer's Paradox", "Collective Action problems", the "Tragedy of the Commons", "Many-Person Prisoner's Dilemma", etc., or, in general, the "Social Dilemmas". The well known, two-person, "Prisoner's Dilemma" is just a special case of the "Social Dilemmas".

    In this essay, these social phenomena, which Garrett Hardin described (see References at end of this essay) as "problems that have no technical solution" (a nice way of saying it is a paradox) and other such problems belonging to the "social dilemmas" (SD), will be represented by one term -- "The Voter's Paradox" (VP). The "Voting Paradox", seems to be an excellent representation of a wide variety of Social Dilemmas.

    The definition for "paradox" used in this essay is "a person, situation, act, etc. that seems to have contradictory or inconsistent qualities" from Webster's dictionary. Basically, what we have are two apparently contradictory truths in the same phenomenon.

    One reason that the Voting Paradox is a good candidate to represent Social Delimmas in general is that it seems to be a double paradox! The first can be expressed as, "while it is true that a particular personal endeavor would return a benefit to all members of the group such that all individuals would receive rewards that, in totality, more than compensate for that individual's contribution, it is also true that that particular individual would receive an even greater net return by not contributing anything!". I will call this the "free-rider" aspect. This aspect of the phenomena is consistent with a related dilemma, the "Prisoner's Dilemma" which has received much study and is well reported in the scientific press (see the associated article, "Prisoner's Dilemma").

    The second paradox is that, "while it is true that the outcome of a group effort is made up of the sum of the individual efforts, in many cases a particular individual's contribution makes no significant and/or measurable impact on the outcome". I will call this the "my vote doesn't count" aspect.

    I will go into more detail on the Voting Paradox, in particular, in the Examples section.

  3. Is Rationality the Problem?
  4. "What is rational is real;
    And what is real is rational
    ". -- Hegel
    The basis for the social dilemmas is rationality. So, what do we mean by "rationality"?

    First, it is considered to be rational for individuals to look after their own best interests. It is hard to imagine that a free individual can do anything else. Now, we know that a computer or robot performs actions without any such "self-interest" motivation. A robot simply does what it is told to do. I suppose a human could also be in a robotic state also, in which case there would be no need for self-interest motivation.

    Hopefully, most of us cannot be described as robots although it sometimes seems that way when you see people mindlessly spending their money for useless products just because a TV salesperson suggests it. Further, a case can be made that people who mindlessly accept directions from others, that is meme-driven people, of which the trend seems to be more of every day, are not much more than robots.

    But for those of us who have not totally succumbed to the euphoric state of the meme-controlled mind, and who still have to make decisions continuously throughout the day, rational self interest has to be the criteria (but maybe we humans are not always rational. See my essay, "Humans are Rational, aren't they?"). Even a person who claims to be an altruist will admit that the reason she wants to help other people is that it makes the her feel good, and therefore, is performing a selfish act.

    A person who gives her money to a robber has the choice of parting with the money or possibly her life. Choosing life over money is a rational self-interested decision.

    With regard to the social dilemmas, the choice is between looking after one's own interest or looking after a large, often anonymous, group's interests. The problem is complicated by the disproportionate impact that the contribution might make between giving it to yourself or the group. For example, maybe I could send in a $1,000 to President Clinton to help with the national debt. That $1,000 means a lot to me but it will have an insignificant impact on our country's welfare and it will not be noticeable by anyone. So, the problem is not just that I am selfish, but that the individuals of the group get little from my contribution compared to what I would get giving it to myself.[2]

    The act of voting that I have chosen to be representative of the social dilemmas, seems to be an irrational act for the individual. It has some cost and it would appear that one vote cannot impact the election results. Some say that there is a rational justification for voting and that is the possibility of breaking a tie. But the probability of breaking a tie in any election of any reasonable size is incredibly small. An excellent analysis of this probability is in the book, Democracy and decision listed in the references at the end of this essay. In any case, tie breaking is not the reason most people vote.

  5. An Action can be both Good for the Individual but Bad for the Group
  6. Specifically, the claim here is that a situation can exist such that: (1) while everyone would be better off if everyone contributes (cooperates), a particular individual is always better off not contributing (defecting) and (2) the individual's contribution will not affect the outcome anyway. That both of these conditions are satisfied for a voter in a national election is obvious on reflection. We are all better off if most people vote, but my vote will make no impact and it does cost me to vote. Hence the term, "Voter's Paradox" for this type of social dilemma.

    The reader should not be too quick to cynically dismiss this assertion as some academic pathological construct. On the contrary, the situation described is extremely common -- as I will attempt to show in this essay by providing examples occurring in all walks of life.

    Philosophers and social scientists claim that the VP is a special case of the well studied "Prisoner's Dilemma" phenomenon. "The Voter's Paradox", is similar to the "The Prisoner's Dilemma" in the payoff matrix (where the "other player" is everyone else) but is much more complex and much more common in the real world.

    The VP phenomenon includes both contributions by an individual to a group shared benefit as well as the withdrawal of some portion of a group shared asset. The "contribution" example is best illustrated by the voting process itself. The "withdrawal" example is well illustrated by the so-call "Tragedy of the Commons" in which excessive withdrawals of a shared asset are done by certain individuals. This aspect is often called "freeloading" or "freeriding".

  7. Some Examples to help Clarify the Concept
  8. Here are a few examples of Social Dilemmas. More are listed here.

  9. Group Size and Anonymity
  10. The VP results from the fact that for the individual there is greater reward for defecting than there is for cooperating. So why do many (most?) people cooperate? One reason is that cooperating can have many hidden rewards. No doubt, most people get a "feel good" reward when they help others or carry out their civic duties. Certainly, they are greatly rewarded if everyone knows about it. If these inner rewards are large enough, then it can become rational to cooperate.

    But therein is a major problem. When mankind consisted of small family of hunter/gatherer groups every person's actions were known by everyone else. Even in modern times, people in small communities cooperate because their actions are displayed to everyone in the community.

    On the other hand, most of us live in large cities in which no one knows or cares what we as individuals do, for the most part. If I send in an extra thousand bucks with my income tax because I really want to help the poor and the military, no one will know. My reward just doesn't come close to my cost, the thousand bucks. That is the situation most of us are in today and that is why defection continues to grow over cooperation.

    The conclusion is obvious and many studies have shown (see the Hubermann reference) that people cooperate more if they are kept in small groups. Large organizations do better if they organize into many small components. People live fuller lives if they live in small towns. A political conclusion can be drawn here: have we done the right thing in centralizing our government in Washington?

  11. Classifying Social Dilemmas
  12. A Basis for Morality?
  13. Like the players of the Prisoner's Dilemma, we are confronted with a situation in which, rationally, an individual should defect (freeride) but we will all suffer if both players (the individual and the "rest of society") take that action. While there are other actions that will help to alleviate the problem, the most promising and most general solution is well known and has a long history: morality.

    If somehow we can establish that cooperating is the moral thing to do and we can convince everyone (or, at least, most everyone) to be moral, then we have solved the problem. People will vote, politicians will not steal, teenagers will avoid irresponsible sex, people will conserve resources or not pollute the environment, and so on.

    Could it be that human society is so constructed that to survive, morality is necessary? An intriguing thought -- a nonreligious basis for morality! And a powerful one: either we cooperate or we face a total destruction of civilization as we know it.

    For more on this issue, see my essay, "A RATIONAL JUSTIFICATION FOR ETHICAL BEHAVIOR".

  14. Solutions: Some Successes, Many Failures
  15. Where to get More Information?
  16. The study of social dilemmas is scattered over several disciplines: Game Theory, Social Science, Philosophy, Economics, Politics, Public Choice Theory, Social Choice Theory, and Computers (Artificial Intelligence). It is not an easy subject to cover. The references I have provided below would provide a good start. I was particularly impressed by the works of the Hardins, Gauthier, Olson, Brennan, Lomasky and Buchanan. There is some stuff on the internet but finding it is not easy due to the subject being spread over so many fields. Much of the stuff on Prisoner's Dilemma, which is readily accessaboe, I feel is not very pertinent to the real world social dilemmas. It seems that the PD is a fun game for academics to play while the social dilemmas are just too messy. However, the PD model is important as a simple representation of the "non-zero-sum" nature of society's many "games".

By: Leon Felkins
Date: 10/14/95


1. The term "Voters Paradox" has already been assigned to another phenomenon involved with preference ordering. Nevertheless, the example of voting is just too good of a representation of the Social Dilemmas to be ignored. Sorry.

2. Parfit (see References) proposes an interesting situation in which a thousand wounded soldiers are dying of thirst in the desert. A thousand altruists each have a pint of water that if each gives to a dying man can save his life. An alternative way of delivering the water would be for each altruist to pour her pint into a water cart and then each man be given his pint from the common water cart. Now the altruist has to realize that by not donating her pint of water, the impact on the men would be imperceptable for each man would now receive one one thousandth less water. This insignificant contribution may make the altruist decide that it is not worth it whereas before her contribution would have saved a life. What changed?

3. For a responsible voter, the major cost of voting is acquiring knowledge of the issues. See Patrick Gunnings on-line book on Public Choice for more info on this important fact.

4. Self interest of public officials is covered under the theory of Public Choice. See the online book by Pat Gunning, identified in the Reference section, below.


Aristotle's "Politics", Written c.a. 350 BC

Axelrod, Robert; The Evolution of Cooperation. Basic Books, New York, 1984.

Brennan, Geoffrey and Lomasky, Loren; Democracy and decision. CAMBRIDGE UNIVERSITY PRESS, New York, 1993

Buchanan, James and Tullock, G.; The Calculus of Concent. University of Michigan press, Ann Arbor, 1962.

Dawkins, Richard; The Selfish Gene. New York: Oxford University Press, 1976.

Gauthier, David. Morals by Agreement. Clarendon Press, Oxford. 1986

Glance, Natalie and Huberman, Bernardo; "Dynamics of social dilemmas". Scientific American. March, 1994 (See their page on Dynamics for some of their simulation results)

Green, Donald P. and Shapiro, Ian. Pathologies of Rational Choice Theory. Yale University Press, New Haven, 1994

Hardin, Garrett, "The Tragedy of the Commons", Science, 162:1243-1248, 1968. (Now online at

Hardin, Russell, Collective Action, Johns Hopkins University Press, Baltimore, 1982.

Lichbach, Mark Irving. The Cooperator's Dilemma. University of Michigan Press, Ann Arbor, 1996.

Lomasky, Loren; "The Booth and Consequences". Reason. November, 1992. A copy is here.

Olson, Mancur. The Logic of Collective Action. Harvard University Press. 1971

Ostrom, Elinor. Governing the Commons. Cambridge University Press, New York, 1990

Parfit, Derek: Reasons and Persons. Clarendon Press. Oxford. 1984.

Ridley, Matt: The Origins of Virtue, Viking. 1997

On the Internet:

My essay, "Voter's Paradox" at this and other sites.

Peter Carter's Essay on "The Student's Dilemma" -- containing experimental results obtained with high school students.

Information on Patrick Gunning's book, UNDERSTANDING DEMOCRACY: An Introduction to Public Choice

Ashlock's and Smucker's paper, The Iterated Prisoner's Dilemma with Choice and Refusal

John O. Ledyard's Public Goods: A Survey of Experimental Research, 1994

Back to "Social Dilemmas" Page.
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