“Your votes count” is an empty slogan or an illusion or a lie. Your vote is usually not counted. I am always amazed to find intelligent people who think that an ordinary voter, using his single vote, has a significant opportunity to influence the outcome and outcome of an election. We meet this idea again in Simon Cooper *financial bar* Column (“The Most Powerful Voters Are Who You Think,” Oct. 3, 2022).

Many people are surprised when an economist or political scientist tells them that a typical and rational voter has no reasonable hope of making an electoral decision, that is, of who will be elected (or what alternative will be adopted in a referendum). If he votes differently or not at all. These people have never reflected on the mathematics of claims, or tried to choose when one vote made a difference, or are so engrossed in a simple democratic ideal that they only imagine a reality that corresponds to it.

Basic math is relatively easy. Consider a committee of three, including yourself, who vote to choose between two alternatives. If the probability that the other two committee members each vote for either option is 0.5, the probability that your vote is decisive is given by the ratio of the total of the four possible outcomes to the two possible tie outcomesâ€”that is, 0.5 also but if the committee has 4 members besides you. , then your probability of being decisive drops to 0.375. If the committee is a group of 1,000 voters, the probability that you are decisive drops to 0.0189. This odds is further reduced if the probability of another voter voting is slightly changed one way or the other. For example, if these probabilities in the two options are 0.49 and 0.51 respectively, we can calculate that, at 1,000 plus your electorate, your probability of breaking a tie drops to 0.0155; 100,000,000 plus in your constituency, which is astronomically low as opposed to the number of particles in the observable universe. (See the sidebar “Does Your Vote Really Count?” in my “The Public Choice Revolution” *regulations*, Fall 2004; Based on Dennis C. Mueller, *Public Choice III* [Cambridge University Press, 2003]pp. 304-306.)

Let me immediately answer a standard objection: “But together, we make a difference.” Of course. If all consumers buy one more tomato, the price of tomatoes and farmers’ revenue will jump. If a voter controls 50%+1 votes, he is sure to be decisive. But the chances will drop dramatically if he controls only 25% of the vote, or 10%, or ultimately, only his own vote. QED.

Another objection is that rare cases occur. Yes, but not often. Following the November 2017 election of Virginia House of Delegates Decree 94, the Republican candidate first held a 10-vote lead with 23,215 ballots cast. A recount changes the result to a one-vote lead for the Democratic candidate. A three-judge panel then erroneously found one vote disqualified, creating a tie. After further litigation and in accordance with Virginia law, a random drawing was held on January 4, which gave victory to the Republican candidate. At best, every Republican voter can claim to have produced a tie, and it was in a relatively small district.

This simple mathematical method has been developed, for example, so that before voting the voter can estimate, especially through opinion polls, whether a certain number of his fellow voters have made up their minds in favor of a candidate or party. This reduces the effective size of the decision set in which the voter in question is competing and increases his probability of being decisive. Still, a single voter is unlikely to change the outcome of a major election. So low that it rarely happens.

Andrew Gelman, Nate Silver, and Aaron Edlin add more real-world complications, such as the electoral college, in district and presidential elections. They used a major opinion poll just before the 2008 presidential election (Obama-McCain) to measure how likely the average American would be that he would be elected president, that is, that another president would be elected without his vote. It ranged from a maximum of 1 in 10 million, depending on location, to an average of 1 in 60 million across the United States. (See “How your vote is likely to make a difference,” *Economic research* 50:2 [April 2012]p. 321-326.)

Gelman et al. It also shows that if a voter in New Mexico could get 5,000 of his fellow voters on his side, he had a 1.3% chance of flipping his (small) state and a 1 in 6,000 chance nationally of flipping the president-elect (from a low-electoral-vote state). . But no ordinary voter is influenced by many others, even though a very popular pundit or media personality or a popular singer may be. Not all voters are equal.

To give some perspective, the average American has an estimated 1 in 60,000,000 chance of winning the jackpot in a Powerball drawing (apparently 1 in 292,000,000) of electing the president they want. We occasionally see someone win the jackpot, but an ordinary voter has never been decisive in a presidential election. All Kuppel can bring up is the Bush-Gore 2000 election, when the difference was a “probably miscounted” 537 votes in Florida. Wikipedia gives better examples, but in a smaller selection. It is true, of course, that we would need a large number of presidential elections to test the 1/60,000,000 probability.

Finally (in this short post), note that a single voter could hypothetically be decisively disappointed because “his” president would break the single promise that motivated the lucky voter.

To be fair to Mr. Cooper, his column was more about the fact that a dual citizenship, which he and his wife both hold, allows one to vote in two different countries. Nevertheless, twice the minus probability of having an effect in two different countries still means a minus probability of having an effect. He should have emphasized instead that the big advantage of dual citizenship is not dual voting, but the possibility to vote with your feet.

I’m not denying that a person has moral reasons to vote, at least to maintain a candidate or contribute to a free society. I am not denying that democracy has advantages. I am simply repeating the basic argument that a person who votes to influence the outcome of an election must suffer from cognitive limitations, or gamble, or enjoy whispering his opinion on the wind.