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The Diabolical Voting Game and How You Should Play It

Written by Subject: Voting and Elections

"If voting changed anything, they'd make it illegal." ~ Emma Goldman
Most folks have never thought about the theory and details of voting and elections. If they had, they would have found that it is a very complex subject and loaded with paradoxical and diabolical aspects. There are several aspects of voting, each with challenging characteristics -- too much to cover in this short article. To really understand all the issues of voting and elections would require the study of many volumes, therefore, I will just introduce the major issues and  provide references for those who would like to pursue the matter further.
First off, Let us Acknowledge that "My Vote Will Have No Impact On the Election Results"
This is a hard pill to swallow for many folks, some of which will never accept it! But bear with me -- there are other reasons for voting which I will get to shortly. The truth is that unless the election has a tie result (or within one vote of being a tie), your vote will not change the result.
There are many ways to see that this is true but probably the simplest is to consider a balance scale with, say, 60 balls in the left pan and 50 balls in the right pan (all balls are of the same weight, just like votes). Now you can add one more ball to the pan of your choice. Will it make any difference as to which way the scale pointer is leaning? No, of course not. Since elections are binary, as the scale is with respect to which way the pointer leans, one vote or one ball will not change that result.

Of course, if the number of representatives of a particular party was determined by the number of votes, then your vote could possibly make some impact. Parliamentary systems tend to use that method. But that is not what we have in the USA. Our system is strictly binary in that no matter how close or how far apart the election results are, only one choice is made -- one person is selected from the group that is on the ballet. Yes, we sometimes provide for "run-off" elections when there is no clear majority (greater than 50% of the votes) for any one person. Nevertheless, the problem remains -- for all practical purposes, your single vote will not  make a difference.

Nevertheless, other considerations may give you an adequate reason to vote.
Why You Still Might Want to Vote
You Believe You Have a Duty to Vote
A case can be made that in a democracy, we all have a duty to vote. We could go further and require people to vote in the same way we require them to keep their lawns mowed and to  have an ID card. But there is a gotcha with requiring citizens to vote and that is a vote is meaningless or dangerous if the citizens make no effort to become knowledgeable of the issues and candidates. That is very much the situation with many voters -- they do no more than watch biased reports or outright propaganda on TV to determine how they should vote.

So, the best we could do then is education and attempt to persuade the populace to first, become informed, and second, to vote.
Do You Have Adequate Knowledge of the Issues and Candidates to Post a Meaningful Vote?
It should be a requirement for voting that the voter actually have some minimum awareness about the options she is voting for. This then would require the voter to actually spend some effort in preparing for the vote. Amazingly, many people seem to be unaware of this logical requirement. I have had many heated arguments with citizens that insist that you must vote even if you are clueless on the issues and candidates. This simply makes no sense and is a bit dangerous. The fact is, however,  most citizens are just not willing to pay the price to become adequately knowledgeable about the candidates and issues. In other words for most citizens, the act of voting itself is about all they will spend any effort for.

On the other hand, since the expected utility is so low, this approach of not spending any time preparing for the vote is actually rational!
Should You Vote No Matter How Awful the Candidates Are?
Of course not! As discussed above, an honest person should vote his/her conscience. If your conscience finds all candidates disgusting and/or incompetent and more, then DON'T VOTE! For a "No Vote" is still a vote, in a way (that is, the lack of a vote impacts the election the same as a vote, practically speaking). Not only is not voting expressing your honest values, but it lets the political establishment know that you think that none of the candidates should be in office or the whole election business is a scam.
"If God wanted us to vote, he would have given us candidates."  ~Jay Leno
The Expected Utility from your Vote
Two ways to look at this:
The Mathematical Expected Utility
Your act of voting can be examined mathematically in the same way you would determine the value of an act of gambling such as buying a lottery ticket. The expected utility of such actions is simply the probability of winning multiplied by the winning reward minus the cost of the bet. For example, if your chance of winning was one in fifty (.02) and the reward was $10, the expected value of winning then would be 10 times .02 which equals 20 cents. If your ticket costs less than 20 cents you should buy it but if it costs more, you should pass.

For voting the terms are the chance that your one vote will decide the election times the reward for you minus your cost of voting. Since the chance that your vote will determine the election result is incredibly small and the cost of voting is not zero (there is your time loss and transportation costs to get to the voting booth plus the cost of studying the candidates and issues), it is extremely rare that this will be a positive utility or payoff.

To further complicate the utility of voting, it is very hard to know what your reward might be. Politicians are notorious for ignoring their promises once they are elected. Further, even if the politician once elected keeps his/her promise, what impact it will have on you is still very uncertain.

A good review article on the expected utility of voting can be found at "Rational Choice and Voter Turnout" by Henry S. Farber, Princeton University. Here is a quote from that article that summarizes the theory:
"Riker and Ordeshook (1968) extend Downs's idea in a useful model of the decision to vote that starts with the rational assumption that individuals will vote if their expected utility from voting is higher than their expected utility from not voting. They specify the difference in expected utilities as R = (B * P) - C + D, where
B is the utility gain from getting the preferred outcome,
P is the probability that the individual's vote will yield the preferred outcome (the probability that the individual is pivotal),
C is the (non-negative) cost of voting, and
D is the positive benefit of the act of voting." (The D term is to capture any other benefits or "feel goods" such as "Duty to Vote", mentioned above)
The Influence of Your Vote on the Candidate
There is another aspect of the election results that might have some potential value to the individual voter and that is that the vote count may persuade the winning politician to act in a certain way. That is, if the politician thinks that what she promised resulted in her getting the majority of the vote, she might see this as a mandate to actually do what she promised to do. This could be seen as a value to the voter.

In that sense, then, the more votes a candidate gets, the more likely she is to carry out her promises (we assume). If that is true, then your vote adds to that total and therefore has some value. Probably not much -- sigh.
What if There Was a Tied Vote?
Our discussion has been on the probability that your vote will break a tie (or cause a tie if one candidate is ahead by one vote), but can this really happen? No. If an election is held that is very close to a tie, it will result in a recount or even possibly another election (or a court decision or even a dice roll). This seems to complicate the simple utility calculation but it really does not. For we can change the scenario to extend it to the probability that your vote will cause a recount or the probability that the recount will be a tie. Practically speaking the problem remains the same.

Unfortunately, for many of us the person we would like to vote for has no chance in hell of tying the likely winner. Some say that voting for a person that has no chance of winning is "wasting your vote". Nonsense.
The Nonsense About Wasting Your Vote
The fact that your vote will not change the results actually is a great plus for you! Now you can simply vote your conscience and not have to worry about your "vote being wasted". Voting for someone or some issue that you don't really believe in is really unethical. For most people, to do so is upsetting and shameful. So, don't bother. Number 1, do your duty and vote and number 2, vote your conscience. I think you will feel a whole lot better about it. Please take a look at this excellent article on this point, "Your Vote Won't Matter. Don't Waste It" by Art Carden.

Strangely, when two candidates are up for election and the polls show that your candidate or issue is highly unlikely to win, hardly anyone will criticize you for voting for your candidate -- they will not say "You are wasting your vote" (actually it doesn't matter if you vote for the winning person or the losing person, your vote still does nothing). But let there be 3 candidates, let's say from the two major parties and a third party that has little chance of winning, and now if you vote for the person representing the third party, many people will accuse you of wasting your vote! Nonsense -- it is all the same -- your vote doesn't count anyway (see references if you still have your doubts).
Influencing Others to Vote
Now we're talking. If you really want to effectively influence an election result, forget about your vote and instead convince thousands of other citizens to vote for your candidate! Really. If you can get 10,000 people to vote your way, your chances of impacting state and local elections is pretty darn good. Influencing the results of the national election might still be unlikely however. In that case, you would want to influence a much larger number of citizens. Nevertheless, influencing others is a rational approach to getting your man or woman in office.
The Impact of the Electoral System in the U.S.
First off, let us get this out of the way; your vote will not count whether there is a straight vote count or there is an "Electoral System" involved. While a system in which results are determined by popular vote would seem to be more honest and straightforward, there is no significant influence on the value of your vote, either way. The Electoral System, however, can result in a person being elected that does not have the majority of votes of the citizens. Not good, but we are stuck with it at the moment.
There is essentially zero chance in your vote making a difference in the election results. Since there is a cost in voting, voting does not appear to be a rational thing to do. However, if you accept that in a democracy, citizens have a duty to vote -- a reasonable belief -- then you should vote. If nearly everyone would do that, then the concept of democracy might actually work somewhat. However, there is a gotcha; before you vote, you must prepare to vote. That means you have to study the issues and candidates and not just listen to the propaganda spewed from the boob tube. Your real research will take more time and effort than voting and therefore is the hard part. Unfortunately, hardly anyone does it adequately.

If you don't bother to study the issues and candidates or if there are issues or candidates that you don't approve of, then don't vote. For not voting counts the same as voting. That is, the person you would have voted for now has one less vote -- which is just the negative of having one more vote.

It is possible, but maybe not probable, that your tiny vote will add one more vote to a total that might influence the candidate to actually keep her promises. The assumption here is that the higher the vote count she gets, the more likely she is to keep her promises. In that sense, your vote counts -- a tiny amount!
Always vote for principle, though you may vote alone, and you may cherish the sweetest reflection that your vote is never lost. ~ John Quincy Adams
References (in no particular order):
Olson, Mancur. The Logic of Collective Action. Harvard University Press. 1971

Donald G. Saari, "The Symmetry and complexity of elections", Also see his book, Basic Geometry of Voting

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

Leon Felkins; "The Voter's Paradox" ,

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

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

P. J. O'Rourke, Don't Vote It Just Encourages the Bastards, Atlantic Monthly Press, 2010

Joel Poindexter, "90 Million Americans Can’t Be Wrong",

Yoon G Kim, "The Mathematics of Voting",

Jeremy Kolassa, "What is a vote?",

Leon Felkins, "How To Avoid 'Wasting Your Vote' ,, Originally published in Spintech Magazine, 2/12/2000

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