Written by Leon Felkins, Copyright 1996
Originally written November, 1994
It is the rule rather than the exception that the cost of a contribution a person would make to some group activity will exceed the benefit that individual might receive in return from being a member of the group. The voting example is a particularly good example of this phenomena in that it can easily be shown that one vote is highly unlikely to provide any measurable benefit whatsoever while there is cost to the person making the vote (admittedly small, usually).
The good news is that people do not always act "rationally" - in the sense just described. In fact, most of the time, enough people cooperate in these situations of public good such that the collective effort does not fail. Why this is so will be examined further on in this essay.
My attempt in this essay is to define the phenomena of the VP and related phenomena as clearly as possible. While it is recognized that the impact of the VP on our daily lives is enormous, the primary purpose of this essay is to present the paradox itself in enough detail such that the phenomena can be clearly understood and evaluated but that purpose does not include a solution to the paradox.
When most people are confronted with the fact that a rational person would not bother to vote because a single vote makes no difference in the outcome of an election, the typical response is "But what if everyone did that"? Upon the most casual examination, the question turns out to be quite ridiculous. If everyone chose not to vote then the election would fail. That's the answer, but it provides no help in solving the problem of the VP.
But let us examine the four possibilities:
1. Everyone else behaves as usual, with most people voting. I can vote or not. Result: whether I vote or not does not impact the result.
2. Everyone else chooses not to vote. I can vote or not, but it doesn't matter as the election will be declared a failure, no matter what. My single vote will not change that.
The fact is, the only time my vote would have any impact on the election is when there is a tie -- a highly unlikely event.(See notes)
Could it be that my avoidance of voting might influence others to do the same? Not very likely. It is very difficult for the private citizen to influence others even if he or she tried. Practically speaking, my actions in any group large enough for anonymity of the individuals, are not likely to have any impact on what others do. Put another way, if massive advertising with powerful media personalities can't always cause the votes to go the desired way, it seems highly improbable that what I do will influence anyone!
Consider a group with two or more members and a situation in which the group as a whole would benefit from certain actions of the individuals in the group. While it is not necessary that the benefits be shared equally, we will assume that all members get some portion of the benefits and that the portion received by a member is not dependent on his/her contribution. The contribution of the individual is voluntary.
Under these conditions, so common to modern society, the payoff to the individual (share of group benefit minus his/her cost) is usually maximum when the individual does nothing at all! That is, when the contribution is voluntary, the highest return to the individual comes from free-riding.
Further, we can assume that if all or most of the members of the group contribute, all members of the group would benefit more than they would if there was no cooperation. That is, if most or all would contribute, the return for each individual is greater than it would be if each kept his or her contribution and proceeded alone. This is a valid assumption since otherwise there would be little reason to cooperate in the first place. (I am not talking about charity or welfare programs here; I'm talking about joint ventures that provide greater return when all or most cooperate than when they do no, such as the PD.)
In summary, in this classic "individuals may volunteer but everyone shares the benefits" scenario, it is evident that the decision to do nothing is always the best strategy regardless of what the rest of the group does since the individual partakes of the benefits whether he or she contributes or not. Yet all would do better if each person cooperated.
The classic definition, as described above, suffers from the criticisms that it is too general, leaves out some additional complicating details, and does not include real world secondary reactions that would impact a "rational" person's reasoning. An example of "complicating details" is the binary nature of elections (to be discussed further below). And many will suggest that secondary effects such as a person's reputation may completely override such "rational" decisions to be uncooperative.
I will try to examine these additional details by extending the definition in several ways.
First, I will examine the "cost/return" function, or the utility function, that defines the net return that a person expects to receive in a cooperative investment. Of course, it is assumed that there will be some return, i.e., the effort will not be a total failure. If there is only a chance of success or failure, the function would have to be modified by the addition of a multiplicative "probability of success" term.
Second, various types of non-linear situations will be examined. For example, elections in which the outcome is binary. That is, the payoff is discreet and not proportional to the contribution. For example, we do not elect a president that is 40% Clinton, 35% Bush and 15% Perot. "Clinton only" is the payoff regardless of the percentages once his percentage of the vote is greater than any of the others.
Thirdly, practicality will be considered. It is reasonable to accept that some returns can be so small as to be insignificant. When the water in Los Angeles is rationed and I violate the order to not take showers, the result to others will not be measurable. And if I feel real patriotic and decide to send Clinton a $1000 to help pay off the national debt - as one student did - the effect on the national debt is not measurable (a monitor on the national debt would not be able to detect that such a small contribution had been made).
Fortunately, it does not require 100 percent cooperation for most group efforts to succeed. Many public projects function with only a small percentage contributing. Voting is a good example.
When a person contributes to a voluntary group effort, whether the effort will fail or succeed should be the first concern. Let us look at the two situations:
Suppose that enough members of the group make a contribution such that the effort succeeds. Then the defecting member will obviously receive maximum return by making no contribution at all.
Alternatively, suppose that essentially all defect. Then the particular contributing individual would lose even more since the return from his/her investment would be zero or worse (if the investment is not returned).
Finally, the definition of cost and the return to the individual for a given action is extended to include any and all internal psychological feelings from the action. The good feeling coming from helping a person in distress or the bad feeling of running away, is part of the cost or payoff of whatever action the person takes and can be substantial.
All of this depends on the concept of being rational which we need to examine first.
What does it mean to be rational? Not an easy question to answer even though the term is used casually by almost everyone.
The theme of this essay is based on the concept that a person's best interests are served by acting rational. Rather complex philosophical arguments can be made that this may not always be the case. For example, some would argue that ignorance is best for most of humanity and evidence from recent history would seem to support this in that it appears that for much of the world, the loss of innocence seems to be closely correlated with diminished happiness.
These arguments lead in to a philosophical morass any study of which would greatly exceed the scope of this article. Therefore, in this essay, we will assume that it is in the best interests of an individual to be rational -- which I will now define for the purposes of this essay.
To make any progress in the study of this apparent dilemma, the concept of "rational behavior" has to be carefully defined. "Rational behavior" means that behavior that would actually provide a good return for the person's contribution - based on the currently available information (an action can be rational even if the information available is faulty or erroneous). This does not require optimality but does require that the return to the individual be at least equal to the cost to the individual. When there are alternate paths to take and a choice must be made, a rational choice would be the one that provides the best actual return to the individual making the choice. When the result is not completely known but can only be predicted with some probability, then a multiplicative probability term must be introduced.
On the basis of this definition, many actions would be classified as irrational even though the person taking the action was rewarded if the person's actions were based on faulty reasoning and/or data.
While there is considerable controversy over just what being rational really means, the Rational Choice theorists generally agree on the following requirements:
It comes as no surprise that a person's perceptions and/or a person's internal programming (i.e., beliefs) can cause irrational behavior - based on the above definition.
The person having unlimited resources is a rarity. By far, most of us are burdened by the fact that every contribution of time and/or resource to any particular action is at the cost to all other actions we might take with that time and/or resource. That is, when we ponder whether we can contribute $10 to some particular activity that would result in some reward, a rational person must consider the impact of the loss of that ten bucks to all other potentially rewarding activities. That is, the cost of a contribution is the cost of opportunity lost for all other possibilities.
How a person reacts to the environment is determined by that person's internal programming. For the purpose of this analysis, that programming is considered to consist of two categories: genes and memes. An excellent discussion on both of these forces is contained in Dr. Dawkin's book, The Selfish Gene and other sources on the Internet. For our purposes here it should be sufficient to say that "memes" are those psychological forces and beliefs that become instilled in a person through learning and societal influences.
In any particular situation, the individual must act on his or her perception of the environment and the expected results of an action being considered. That these perceptions are likely to be in serious error in many situations, is no surprise to anyone. The available data is almost always incomplete and often contaminated by others who wish to control the individual's action. Further, the analysis of this data by the individual is usually flawed due to the confused and improper internal programming of the individual making the analysis.
Of course, people don't act on just material rewards alone. The benefits that a person receives come in many forms, but the most common non-material benefit is likely to be "good feelings".
The good feelings that many get from making a contribution to the public welfare may be substantial and may considerably exceed the cost of that contribution. Most people among other things, whether the action is "good" and how will their reputation be impacted. That the beliefs of a person may be misguided is of no consequence for this analysis.
Many people are motivated to contribute to a group activity if they believe that the activity is honest and useful.
"How will I be regarded by the rest of the community for the action I am about to take?" is a very powerful consideration for most people. Note, however, this powerful influence fades away when the community is large and the individual's actions are unknown or unnoticed by anyone else.
The good feeling we get from doing any particular action is completely determined by the genes and memes we may possess at that time.
The psychological environment that a person is subject to has a great impact on the feelings that a person has about doing or not doing a specific act. For example, in World War II, a group of soldiers boarding a landing boat in preparation to attack an enemy occupied beach, knowing that there is little chance of survival, still do it. That is because that action is the only acceptable action in that current environment. But times change; in more recent wars, soldiers have refused to fight because the pressure to do so was not so great. Apparently the meme that says you should willingly give your life for your country has diminished in force over the years.
Whether we take a particular action or not is determined by what we believe the values of the variables in the cost-return equation to be - not what they might actually turn out to be. Our beliefs can change the perceived values of these factors enormously.
Much cooperative activity that would be deemed as irrational, if all facts were known, may be still carried out if the future result is not known for certain but only as a probability. While a person would most likely not bother to vote if he or she knew that the potential winner was thousands of votes ahead and he/she was the only one left to vote, that person would still vote if the election details were still unknown or still to be determined even though there was reliable information that one of the candidates is expected to win by thousands of votes. For much of the population, "as long as there is some chance" that their vote will "count", they vote without regard for the incredibly small probabilities involved.
Some people apparently believe that their actions will encourage others to do the same. This belief greatly impacts the perceived value of the group benefit.
The story of the motorist in distress given in the introduction to this essay is a good example. My wife wanted to help because we might need help in a similar situation in the future.
This implies that the person receiving the help will tell others of our act of compassion. They might, but will the word spread? Well, it doesn't seem to. Such acts happen all the time but they get little publicity. On the other hand, we constantly hear of robberies and mayhem.
We have to conclude that an individual act of compassion is not likely to have much impact on the mores of society in general.
When and if my car breaks down, there will be no noticeable result of my assistance given to a stranded motorist years ago in a strange city.
If cooperating is more beneficial to the group and its members, but cooperating is irrational for the individual, then ignorance (or "extra-rational", per Hardin) can actually be best for the group - a concept well known by governments and religions.
In an effort to overcome the limitations imposed by the VP, leaders will often attempt to alter the perception of the values to be received. For example, we are constantly told that our vote will make a difference when in fact, a single vote makes no significant impact on any election. In this case, the resulting perception, which the person is actually deceived about, is a "good" since that person will vote.
For a good introduction to this issue, see Loren Lomasky's review essay, What Do People Really Want?, a review of Timur Kuran's book, Private Truths, Public Lies.
When the fact that individuals may have opposing public and private preferences is combined with another phenomenon, the "my vote doesn't count" belief, then we have a real problem. Person's who express a public view different from their private view may feel that the effect of their expression -- including voting -- is nil and therefore not likely to impact any group results. That this in fact happened in the voting for the Constitutional amendment that imposed Prohibition (the 18th Amendment)on the US is the thesis of the essay, "The prohibition-repeal amendments: A natural experiment in interest group influence", Public Choice 90:139-163, 1997, by Michael Munger and Thomas Schaller. I quote:
"The conflict between the two types of preference is particularly severe when political decisions are being made, because citizens (rationally) do not perceive that their own statements have any nonnegligible influence on the collective outcome. Since the probability of any one persons's vote, or opinion, determining the outcome is zero as the number of decision-makers grows large, each individual simply accepts the outcome as given and decides what preference that should project to others in their church, community, or other group."
2. However, it is well known that humans are notoriously inaccurate in evaluating expected value, usually choosing a sure thing of less expected value, if available, over a probable thing of greater expected value. This is commonly referred to as "risk aversion". See the Stanford Encyclopedia of Philosophy for a description of this issue.
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