“Your vote counts” is an empty slogan or an illusion or a lie. Typically, your vote does not count at all. I am always surprised to find intelligent people who think that an ordinary voter, by using his single vote, has a significant chance of influencing the outcome and consequences of an election. We meet this idea again in Simon Kuper’s Financial Times column (“The Most Powerful Voters Aren’t Who You Think,” October 3, 2022).
Many people seem surprised when an economist or political scientist tells them that, with his single vote, an ordinary and rational voter has no reasonable hope of deciding an election, that is, of changing who is elected (or which proposition is adopted in a referendum) compared to what would have been the case had he voted differently or not at all. Some people either have never reflected on the mathematics of voting, or have never tried to find elections where one vote made a difference, or perhaps they are so engrossed in a simple democratic ideology that they just imagine a reality that matches it.
The basic math are relatively simple. Consider a committee of three persons, including you, who vote between two alternatives. If the probability that each of the other two committee members votes for either alternative is 0.5, the probability that your voice will be decisive is given by the ratio of the two possible tied results to the total number of four possible outcomes, that is, 0.5 also. But if the committee has 4 members besides you, your probability of being decisive decreases to 0.375. If the committee is a group of 1,000 voters plus you, the probability that you will be decisive drops to 0.0189. These probabilities decrease dramatically if the probability of every other voter’s voting one way or the other changes only slightly. For example, if this probability is respectively 0.49 and 0.51 for the two candidates, we can calculate that, in an electorate of 1,000 plus you, the probability that you will break a tie goes down to 0.0155; in an electorate of 100,000,000 plus you, it is astronomically lower that the inverse of the number of particles in the observable universe. (See the sidebar “Does Your Vote Really Count?” in my “The Public Choice Revolution,” Regulation, Fall 2004; see also Dennis C. Mueller, Public Choice III [Cambridge University Press, 2003], pp. 304-306.)
Let me answer a standard objection immediately: “But all together, we make a difference.” Of course. If every consumer buys one more tomato, the price of tomatoes and the growers’ incomes will jump. If one voter controlled the votes of 50%+1 of the electors, he would be decisive with certainty. But the probability would drop dramatically if he only controlled 25% of the votes, or 10%; or, ultimately, only his own vote. QED.
Another objection is that rare events do happen. Yes, but not often. Following the November 2017 election in Dictrict 94 for the Virginia House of Delegates, the Republican candidate had a 10-vote lead on all 23,215 ballots. A recount changed the result to a one-vote lead for the Democratic candidate. A three-judge panel then found a vote incorrectly disqualified, which produced a tie. After further litigation and according to Virginia law, a random drawing was held on January 4, which gave the victory to the Republican candidate. At best, every Republican voter can claim to have produced a tie, and that was in a relatively small district.
This simple mathematical approach has been improved, for example by considering that the voter can guess, notably through opinion polls, that a certain number of his fellow voters have dug their heels for a candidate or a party, which decreases the effective size of the decisive set in which he is competing and increases his chances of being decisive. Yet, the probability that a single voter changes the result of a large election remains very low. So low that it very seldom happens.
Considering more real-world complications, namely the districts and the electoral college, Andrew Gelman, Nate Silver, and Aaron Edlin used the 2008 presidential election (Obama-McCain) to evaluate what probability the average American could have reasonable formed that he could elect the president, i.e., that without his vote another president would be elected. It was at most 1 in 10,000,000 depending on locations, and 1 in 60,000,000 million on average over the United States. (See “What Is the Probability Your Vote Will Make a Difference,” Economic Inquiry 50:2 [April 2012], 321-326.)
Gelman et al. also calculated that if a voter in New Mexico could have brought 5,000 of his fellow voters to switch from the other side to his, he would have had a 1.3% chance of flipping the state and a 1 chance in 6,000 of changing the nationally-elected president. No ordinary voter influences that many votes, although a very popular pundit or media personality or sports player or singer may. Not all voters are equal.
To give some perspective, the estimated 1-in-60,000,000 chance of an average American to elect the president he wants is still five times higher than his odds of winning the jackpot in a Powerball drawing (apparently 1 in 292,000,000). We do occasionally see somebody winning the jackpot, but an ordinary voter has never been decisive in a presidential election. The best that Kuper can find is the Bush-Gore 2000 election, when the difference was of “537 possibly miscounted” votes in Florida; Wikipedia would have provided him with better examples, albeit in smaller elections. It is true, of course, that we would need a large number of presidential elections before we can test the 1/60,000,000 probability.
Finally (in this short post), note that the hypothetically decisive voter may end up disappointed because “his” president would break the single promise that motivated the lucky voter.
To be fair to Mr. Kuper, his column was more about the fact that a double citizenship, which both he and his wife hold, allows one to vote in two different countries. Yet, twice a minuscule probability of having an influence in two different countries still means a minuscule probability of having an influence. He should instead have emphasized that the great benefit of double citizenship is not a double vote but the possibility of voting with one’s feet.
I am not denying that there are moral reasons for an individual to vote, at least for a candidate who is very likely to contribute to the maintenance, regeneration, or creation of a free society. I am not denying either that democracy has advantages. I am just reiterating the basic argument that an individual who votes to influence the outcome of an election in anything but a small committee must suffer from cognitive limitation or love gambling. A voter may also just enjoy whispering his opinion to the winds. (See Geoffrey Brennan and Loren Lomasky, Democracy and Decision: The Pure Theory of Electoral preferences [Cambridge University Press, 1993].)
READER COMMENTS
Matthew W Anelli
Nov 6 2022 at 12:53pm
What about the expected value? If one candidate is way better than the other, then voting may be worth it, despite the tiny odds of influencing the vote.
Pierre Lemieux
Nov 6 2022 at 1:09pm
Matthew: Good question. I did not get into this issue specifically. In certain cases, your objection would be valid. If your vote for A has an infinitesimal but positive probability of bringing you an infinite benefit, you would vote for A. The Coastal “liberals” obviously don’t think that this is anywhere true, so they vote their opinion (the beauty of collectivism) instead of their interests (lower tax rates on their high incomes). And note the reference to gambling in my post.
vince
Nov 6 2022 at 1:46pm
If your vote doesn’t count, then don’t bother to vote? If everyone took that approach, then a single vote would count.
Jon Murphy
Nov 6 2022 at 2:02pm
One of my grad professors, the late Walter E. Williams, had a great story along these lines.
He was being interviewed for some program (I do not remember which). The exchange went like this:
Interviewer: “You say that you do not vote because a single vote does not matter.”
Walter Williams: “That is correct.”
Interviewer: “What would happen if everyone thought like that?”
Walter Williams: “Then I would vote!”
Kevin Corcoran
Nov 6 2022 at 4:22pm
When I was in the Marines, I had a lieutenant say something similar to me – “You don’t vote? But what if everyone else did the same thing?” However, this same lieutenant had also told me in conversation earlier that he and his wife had decided to never have kids. So I pointed out to him what his “what if everyone else did that” argument would mean if he applied it consistently. After all, he decided to not have any children – and if everyone else did the same thing, it would lead to the extinction of the human race within a generation! Therefore he should either have children, or just admit he wants humanity to die. He was unamused, but I thought it was pretty funny.
Pierre Lemieux
Nov 6 2022 at 4:40pm
Vince: Yes, if nobody voted. An altruist who, for example, wanted the underprivileged to have more power, may choose not to vote. But then note that, except if nobody at all had voted, his non-vote wouldn’t count.
Note a slightly different thing. If nobody bought potatoes, they would be (temporarily) very inexpensive for the poor. “If everybody took that approach” is a good Kantian rule, but in many cases, whether one person follows it or not has no effect on the social configuration.
diz
Nov 8 2022 at 4:10pm
I would simply argue this is not a reasonable expectation. Most objections to the mathematics of voting tend to be highly unreasonable. Many people will even argue as if my not voting will cause hundreds of other people not to vote. I’m reasonably convinced all other things being equal my not voting will only cause there to be one fewer vote.
Now on the other hand, writing an article like this…
Jon Murphy
Nov 6 2022 at 2:15pm
I tell my students that, in most cases, their vote does count. Namely, it counts in the sense that when you take your ballot and slip it into the machine, a little counter on the side goes up by one. Thus, the ballot counts and has been counted.
Knut P. Heen
Nov 9 2022 at 11:52am
I tell my students that I vote for the communists just to prove that my vote is worthless.
Scott Sumner
Nov 6 2022 at 2:40pm
You said:
“I am just reiterating the basic argument that an individual who votes to influence the outcome of an election in anything but a small committee must suffer from cognitive limitation or love gambling.”
I don’t follow this point. I’ve never met anyone in my entire life that thought their vote was likely to be the deciding vote in an election, but it is perfectly rational to vote with the intention of influencing an election. Each voter contributes in a small way to the outcome. The influence may be small, but it is not zero.
Also keep in mind that votes can matter even if they are not decisive in any particular election. The margin of victory also affects the behavior or politicians.
vince
Nov 6 2022 at 4:06pm
“Also keep in mind that votes can matter even if they are not decisive in any particular election. The margin of victory also affects the behavior or politicians.”
That’s right. Every vote expresses an opinion. Winning 90-10 is a completely different message than 51-49.
robc
Nov 7 2022 at 12:31am
There is no size of vote for which my vote can shift the result from 52-49 to 90-10.
If it is 90-10 after my vote, it was, at my highest influence, either 89-11 or, more likely, 100-0 before my vote. With my voting history the latter is much more likely.
Dylan
Nov 7 2022 at 7:02am
And this expresses the flaw in the libertarian way of thinking. Yu’re thinking as if you are a lone individual, but you’re not, you’re part of some group. If the group you’re part of is large enough and with similar enough preferences and has more motivation to vote than the other group, then you can definitely sway the outcome or at least make it, far less decisive than it otherwise would be.
Jon Murphy
Nov 7 2022 at 8:23am
No, he’s making a mathematical point. One vote only affects the margin by one vote. This mathematical fact is true whether one is part of a group or not.
robc
Nov 7 2022 at 10:54am
I vote, but I am realistic.
And if something super important came up on my way to the polls, I would easily blow off voting for not mattering. And that doesn’t affect my “group vote” at all.
Also, my group is utterly ineffective. I am voting straight LP as much as possible. I am more interested in voting for allowing wine sales in grocery stores, and that will pass just fine without me.
robc
Nov 7 2022 at 11:46am
I refer back to my rule #2 of libertarianism — No two libertarians agree on anything.
My voting or not voting, in no way affects the behavior of my “group”. If anything it is counter-productive, as it is more likely to change the behavior of that group in the opposite direction, purely out of contrariness.
Jose Pablo
Nov 7 2022 at 8:18pm
” you’re part of some group”
I am part of so many groups I have stopped counting.
But a group I am definitely no part of is the “group of people in agreement with all the unknown policies a particular candidate is going to implement” and I am not part of the “group of people in agreement with all the policies a particular candidate says he/she is going to implement“, either.
I am, for sure, part of the “group of people that knows that the policies the candidate says he/she is going to implement and the ones he/she is actually going to implement are significantly different” and I am also part of the “sub-group of people that knows that the difference between the two sets of policies are a) huge and b) impossible to know beforehand”
As I said: I am part of so many groups that I am pretty sure I am the only individual being part of all these groups I am part of … I guess that makes me an “individual”
Dylan
Nov 8 2022 at 6:57am
I said that somewhat tongue in cheek, for libertarians do tend to be both individualistic and perhaps even contrarian group of people out there. Which could be why they have trouble winning elections, even while (moderate) versions of their preferred policies are likely favored by a majority.
Jose Pablo
Nov 8 2022 at 9:17am
I agree with Robc’s rule #2 but, in any case, is not about being “individualistic”. There is nothing “un-libertarian” in the individual being part of many groups (even being part of the “group of people that decided to give 45%+ of their earnings to a common pot to be used for the common good of the group as envisaged/decided by a bunch of elected representatives among the members of the group“).
A key condition, in any case, is the individual voluntarily choosing to be part of the group and having the right to withdraw from the group at any time (following the procedures and obligation established when voluntarily joining).
Is the idea of being “forced” into a group or being “bonded to death” to it, just because of the circumstances of my birthing, which I have serious problems with. I wouldn’t call this to be “individualistic” more to be “opposed to group forced feeding”.
Pierre Lemieux
Nov 8 2022 at 2:47pm
Jose: RE: Your post starting with the quote “you’re part of some group.” Impressive argument! Perhaps we can can add, in a Russell-paradox manner, that neither you nor any other individual can be a member of all groups (the perfect groupist, the ultimate collectivist), because there is at least one group he cannot be a member of: the group of all individuals who don’t want him in their group. And if you consider all the groups who don’t want Xi (i=1, 2, 3, …, N) as a member in a N-member society, it looks like no two individuals can be members of the same voluntary groups.
Pierre Lemieux
Nov 8 2022 at 3:03pm
In reply to Jose Re: post starting with “I agree with Robc’s rule #2 “. I once thought like this until, after many decades of struggling with Buchanan, I realized he must be taken seriously. The problem can be illustrated this way: Which rational individual wouldn’t implicitly want to be member of a group that would improve his security against a tyrant and war criminal such as Vladamir Putin? The basic argument, if you want to try the red pill, is echoed in my review of Buchanan and Tullock’s The Calculus of Consent. A technically easier way to swallow the red pill, which is how I took it nearly four decades ago, is to read his The Limits of Liberty (which I also reviewed on Econlib). Of course, if moved by another pill, I could still change my mind (I hope)!
Pierre Lemieux
Nov 6 2022 at 4:49pm
Scott: It is true that “the influence may be small, but it is not zero.” In fact, in any large election it is not only small, it is infinitesimal.
On the margin of victory, yes the difference between a one-vote victory and a 1,000-vote victory may make a difference on the behavior of the victor(s), and probably did in the extreme case of District 94! But no voter could have had a significant influence on the margin of victory either (except for a popular pundit, etc.).
vince
Nov 6 2022 at 5:05pm
Instead of “… Your Vote Doesn’t Count” a less disputable title would be ” … Your Vote Won’t be the Deciding Vote.”
Jose Pablo
Nov 7 2022 at 8:25pm
4th acceptation of “count” (using here the Oxford Dictionary): “Be significant”
Using this definition Pierre’s title is not disputable at all.
(And I tend to believe this is the meaning that Kuper was using in the FT)
Avalon
Nov 8 2022 at 6:41pm
Vince-
You are getting to it. The term “Deciding Vote” is getting towards the straw man argument, reinforced by the scientistic statistical gloss. The electoral process does not have a thing called a “deciding vote.” The concept is entirely smuggled in. Pierre’s title is only disputable if count is taken in the ordinary sense that most people would understand it.
Mark Z
Nov 7 2022 at 1:25am
I think the point is that your vote’s expected value is so small that it’s highly unlikely that it’s worth the time and effort it takes to vote; akin to driving all the way across town to donate a nickel to a charity.
Pajser
Nov 6 2022 at 4:49pm
What Scott said. For most collective projects there is no individual whose contribution would be “decisive.” Imagine a group of twenty people carrying a heavy load. Whose contribution is decisive? There is no such man. But they carry that load anyway, thus, they affect the outcome.
Pierre Lemieux
Nov 6 2022 at 5:04pm
Pajser: That’s the problem of collective action, well analyzed by Olson. And again, it depends on the size of the committee. It may be (relatively) easy, with selective incentives, to bring 20 people to cooperate. The problem is what happens as the number of committee members increases. In the most mediatized election, the presidential election, two-thirds of the voters don’t vote. This proportion is even larger in municipal or school elections, which wouldn’t be the case if voting was a was a function of the influence of the voter’s participation. This is a universal phenomenon.
Pajser
Nov 8 2022 at 4:20am
The point is, collective actions (including voting) succeed or fail although usually there is no single individual whose contribution is decisive (in the sense used in article).
Therefore, the voters have no reason to wonder whether their contribution is decisive. It cannot matter, if elections usually end without a single decisive vote.
It may be unexpected, counterintuitive conclusion, but it is logically valid and voters do recognize that.
The USA has a low turnout, but it is the cultural specificity of that country. It cannot be the consequence of the lack of the decisiveness of individual vote because many countries have much higher turnouts.
Pierre Lemieux
Nov 9 2022 at 12:04pm
Pajser: A low turnout is not really an American specificity. For example, in the last French election, the turnout (second round), which was unusually high, was 72%; in the recent Italian parliamentary election, it was 64%.
MikeP
Nov 6 2022 at 5:23pm
I once voted for the winning candidate in a state senate Libertarian Party primary, and she went on to win 82-80. So if I hadn’t voted, it would not have made a difference. But if I had voted differently, it would have gone to a coin flip.
That said, I live in California, so my vote truly does not count this November. I will once again put a pile of unmarked voting sheets into the scanner and will have to override the warning generated for each.
Do you know what people in the so-called undemocratic state of Georgia can do that I can’t this November? They can vote for someone they actually want for office. I can’t. I live in a state where the voters’ choices are constrained by a top-two primary. When is the national media going to notice how Californians’ ability to vote has been completely abrogated by the state? Talk about undemocratic…
Craig
Nov 6 2022 at 8:03pm
Secessio plebis. Vote with your feet. Now that is a vote that will change your stars.
Dylan
Nov 7 2022 at 7:08am
Isn’t it a top two general? And, doesn’t that mean that you get a wider variety of candidates that you can vote for in the primary? In my state, I am not permitted to vote in the primary, which is the only election that matters. By the time it comes to the general election the outcome has already been decided in all but a handful of elections.
Craig
Nov 6 2022 at 8:00pm
I voted when I was younger but fell out of voting in 2000 when my NYC commute overlapped NJ’s poll hours. I moved intrastate in 2005 and I noted that the occasional jury summons continued to go to my parents’ address notwithstanding fact I had a DL and filed taxes from new address. NJ would pay $5 per day for jury duty, not even worth the gas to Morristown and a jury duty summons to an old address isn’t good enough and so I didn’t show. What’s the value of voting? Well, its less than a day’s wage, that’s for sure because I didn’t re-register in the new town. Getting out of jury duty was worth giving up my vote.
Moving to FL I did reregister and voted once but I did so only because early voting let me go at a time which didn’t interfere with work. Since then I have not registered in TN since I remain primary resident of FL and interestingly the voting district in TN has local elections where my vote as a % of the local vote is very low, but even so no way I’d give up my FL homestead exemption just to cast a vote in TN.
Is voting priceless? Perhaps, but for sure one can say its also very near worthless as well.
Craig
Nov 6 2022 at 9:25pm
And if you’re going to burn the gas, do yourself a favor and burn it to go and get a Powerball ticket.
Don Boudreaux
Nov 7 2022 at 5:48am
Nice post, Pierre.
I have never understood why the point that Pierre makes here carries with it the least bit of controversy. To me, it’s in the same epistemic category as “gravity doesn’t take take off for the holidays” or “2+2=4.” That is, the validity of the point seems undeniable.
And while Scott, in his comment, is correct that no voter actually believes that his or her vote will swing the election, the relevance of Pierre’s post is revealed by Vince’s comment – namely, that by voting each voter adds heft to his or her preferred-candidates’ victory (or reduces the size of his or her preferred-candidates’ losses). Vince’s comment, however, misses the truth in Pierre’s post.
Just as no voter can reasonably expect to determine an election’s outcome, no single vote will have an impact on the size of a candidate’s victory or loss sufficiently large to entice that voter cast a vote that’s informed and ‘rational’ rather than a vote that’s uninformed and ‘irrational’ (per Bryan Caplan).
The entire point of scholars such as Anthony Downs, Gordon Tullock, Dwight Lee, Geoff Brennan and Loren Lomasky, and Bryan Caplan noting the insignificance of each vote in political elections is to reveal the resulting perverse incentives on each voter – perverse incentives that are at odds with the high-school civics view of democracy. And so when Scott correctly says that no voter really believes that his or her vote will swing an election, he joins with Downs, Lemieux, et al., in recognizing the reality that there is no good reason to believe that voters vote with sufficient knowledge or care to make the outcomes of elections comparable in their rationality and respectability to the outcomes of individuals who choose in commercial markets.
vince
Nov 7 2022 at 11:39am
“Vince’s comment, however, misses the truth in Pierre’s post.”
I don’t disagree that a single voter should expect to decide an outcome. Of course that’s true. But, to me, that’s not the same as saying your vote doesn’t count. What’s the point of the article, that a reasonable person shouldn’t bother to vote?
MarkW
Nov 7 2022 at 11:44am
Off topic, Don, but maybe you should weigh in on David Henderson’s post (about inflation measurement and product quality). It’s a shame that your Sears catalog comparisons are no longer possible due the Sears’ demise. I wonder how that could be replicated now. Is possible to search Amazon as of, say, November 2002?
Pierre Lemieux
Nov 7 2022 at 1:22pm
Vince: Please reread the last paragraph of my post.
vince
Nov 7 2022 at 2:06pm
No wonder that libertarians lose elections 😉
vince
Nov 7 2022 at 2:30pm
” To me, it’s in the same epistemic category as … “2+2=4.””
Just trying to have some fun here. Given: 1 vote = 0 votes. Then 1+1 = 0 votes. And 1+1+ … = 0 votes. Each individual vote doesn’t count.
Avalon
Nov 8 2022 at 7:23pm
DB>> To me, it’s in the same epistemic category as … “2+2=4.”
vince>> Just trying to have some fun here. Given: 1 vote = 0 votes. Then 1+1 = 0 votes. And 1+1+ … = 0 votes. Each individual vote doesn’t count.
That is funny. Don might want to take that one back.
Jose Pablo
Nov 7 2022 at 9:38pm
“voters vote with sufficient knowledge or care to make the outcomes of elections comparable in their rationality and respectability to the outcomes of individuals who choose in commercial markets.”
Is that even possible?
I would argue that it is impossible to make the rationality and respectability of the outcomes of elections comparable to the outcomes of the commercial markets.
It is not a matter of “knowledge”. Even with all the “knowledge” that can be acquired with access to all the available information about candidates a) the future behavior of this candidate is impossible to predict ex-ante and b) how this behavior affects me as an individual is also impossible to predict (we don’t have the right models to do so. Even with access to all available knowledge on the topic).
It is not only that the vote of any given individual does not count, and it is not only that individuals vote from the most profound ignorance of the candidate policies or even names, and it is not only that they vote subjected to the most irrational bias. The worst part is that the task that the high-school civics view of democracy places uppon voters, is impossible to achieve even to a rational individual in possession of all the actually existing knowledge.
To say: “there is no good reason to believe that voters vote with sufficient knowledge or care to make the outcomes of elections comparable in their rationality and respectability to the outcomes of individuals who choose in commercial markets”, sure qualifies as the biggest understatement of the millennia.
BC
Nov 7 2022 at 8:06am
Even more puzzling is why so many people encourage others to vote and/or seem so annoyed by low voter turnout. The lower the turnout, the more one’s own vote matters. Even more empty than the slogan, “Your vote counts,” is the slogan, “You have a civic duty to vote.” As mentioned in one of Pierre’s comments above, not voting is more altruistic and civic minded then voting because not voting increases (ever so slightly) the power of one’s fellow citizens’ votes.
On the other hand, the fact that so many people encourage others to vote may not be so puzzling after all when one considers that one’s own vote is unlikely to matter. A la Bryan Caplan and others mentioned in Don Boudreaux’s comment, if people recognize that their own vote is unlikely to matter, they won’t mind diluting it infinitesimally more by encouraging everyone else to vote. Instead, other considerations will drive them such as Social Desirability Bias. It’s easy to say the Socially Desirable thing (“Get out and vote!”) when one recognizes that the dilution effect on one’s own vote is tiny.
MarkW
Nov 7 2022 at 11:32am
I had the same ‘what if everybody thought that way’? Discussion with a friend last night. My answer was, ‘If everybody did that, we’d have much more interesting elections’ and ‘But there’s no chance in hell that everybody would think like that’. I also told him that in statewide and national elections, not only is vanishingly unlikely that my (3rd party or non-vote) could turn the election, but it’s impossible, since in any sufficiently close election, the results will turn on legal decisions about which ballots to count (e.g. illegible signature, unreadable postmark, etc, etc)
What I didn’t say is that I believe that holding your nose and voting for the lesser evil tends to make you feel (and even act), to some extent, complicit in whatever misdeeds the lesser evil later commits. It’s a common human tendency to want to defend and feel good about past decisions. It’s why people sometimes become ‘fanbois’ for particular products or companies and tend to exaggerate their virtues and excuse their faults. They unconsciously incorporate the choice into their identity. It’s a variation of Virginia Postrel’s “I like that / I’m like that” — something along the lines of “I chose that / I’m like that”. Now I’m an associate member of the group that made the same choice. I think the tendency is much stronger when it comes to voting.
Mark Z
Nov 7 2022 at 8:32pm
We should wish everybody thought like this. If very few people voted, then not only would voting matter more to those that did, but because of that, they’d have a stronger incentive to garner enough information to be able to be able to vote somewhat rationally. In general, more informed voters tend to be the ones who vote most consistently, so expanding voter turnout means both more uninformed voters and less reason to think rationally about voting.
This is why I hate the ‘pro-voting’ sentiment. Democracy at its best would probably mean only a modest, well-informed minority of citizens bother to vote. The vast majority of people simply have nothing to contribute to politics.
MarkW
Nov 7 2022 at 9:21pm
One of my crazy, never to be adopted, election ideas is that voters for each election would be chosen randomly some months before the election. Only a relatively small, but representative fraction of the electorate would be chosen to vote each cycle. Those selected would have more incentive to pay attention and the rest of us could relax and take the election off (while reducing our tendency toward political tribalism). This approach has maybe a faint similarity to how the Doge of Venice was elected.
Mark Z
Nov 8 2022 at 1:53pm
Thanks for the link, very interesting. Rather similar to juries, which presumably (I hope at least) reach the right conclusion more often than democratic electorates for that reason: when you’re one of 12 people who have someone’s life in your hands you have a very good reason to be careful and dispassionate; and you’re literally forced to observe all the evidence.
Jon Murphy
Nov 7 2022 at 1:56pm
I like this paragraph. When I discussed voting and Public Choice in my classes last week, I likened it to the perfectly competitive market. I said: “There are many reasons to participate in a perfectly competitive market. But you’re not going to influence the price.”
Pierre Lemieux
Nov 7 2022 at 7:32pm
Jon: That’s an important parallel, you’re right. The difference, of course, is that the consumer who pays the price gets the good even if 99% of the other consumers don’t like the stuff and don’t buy it; while the voter who votes only gets the good if at least 50% of the other voters agree with him. (In a multiparty election, he might get away with the approval of less than 50%; in a proportional-representation system, he needs the approval of the coalition that will control parliament, which typically “represents” more than 50% of the voters.)
Jose Pablo
Nov 7 2022 at 8:52pm
As you pointed out in your post, Pierre, you never get the policies that you like, even if your vote agrees with at least 50% of the other voters’ vote.
Afterall, we don’t get to vote policies (for the most part), we vote “unpredictable candidates” that support a (generally quite big) package of policies that I find a) impossible to know before hand and b) impossible to agree with all of them at the same time.
And maybe there are moral reasons to vote. But there are, also, moral reasons for not voting since voting gives democratic government the appearance of a legitimacy it does not have.
A government supported by a 1% percent turnout is easy to be seen as the entity with no right to coerce the individual that any government is. You could argue that contributing to underline the lack of legitimacy of any government (democratic of otherwise) is a moral duty.
Avalon
Nov 8 2022 at 6:28pm
The main problem with voting is it is poor way of expressing preferences. Every year at this season the Sophisticates “remind us of our follies.” (Voting may be folly, but the answer isn’t in the article.)
“Typically, your vote does not count at all.”
I take this literally as it is plainly stated and cannot agree: it is counted. Unless there are serious questions about election integrity, a ballot filed has a very high probability of being counted. (The question turns to “decisiveness” and whether to accept a smuggled definition of “count.”)
“If one voter controlled the votes of 50%+1 of the electors, he would be decisive with certainty.” The “control” POV is astonishing. In effect, Prof. Lemieux claims there is a so-called thing as a “single winning vote”: The “one voter controlled” the other like-kind votes.) There is no basis for this POV, but the entire scientistic argument built on a straw man rests here. There is no definition in electoral politics of “single winning votes” that I am aware of. *All* the determining votes are winning (decisive).
If we want to put “how a vote counts” up to numerical analysis, there are other ways of framing it, and perhaps more valid. Because liberties have been taken, I will also make one up.
Suppose we have an election where 50% wins and there are two choices, A and B. Given is 1000 valid votes were cast. In the final tally, A gets 457 votes and B gets 543.
It turns out the “first” 501 votes for B votes were decisive as the final total count was 1000. In a sense, each of those first 501 votes for B turned out to be “100% effective” (decisive) in B’s victory. “Those 501 votes counted” so to speak. What about the other 42 votes for B and 457 for A? Were they decisive? The 457 votes for A were each 100% important (decisive?) in setting the barrier for B to win (501), as were the other 42 votes for B. One could set a subjective valuation for winning votes if it is not known exactly which vote was counted when (the order of votes counted). That is, we could fractionally dilute winning decisiveness: 501/543=0.92265 “fractional decisiveness.” This subjective valuation is at least as valid as the article’s statistical gloss. Or maybe it is better and more reflective of the reality.
The above could be reconsidered with plurality rather than 50%, but the point is the definition of “counted vote” must somehow reflect the reality of elections. I reckon Prof. Lemieux’s construction can be taken by readers as anything between specious to devastating. I lean to the former. Filed.
Jose Pablo
Nov 9 2022 at 9:52am
“cannot agree: it is counted”
There is a big difference between “count” and “being counted”. For instance, you sure “are counted” when joining the Russian army in Ukraine but I very much doubt you “count”.
Same with your vote: it is, very likely, counted but it does not count at all.
[The Russian army example is not that far from the elections dynamics as it could seem at first sight]
Avalon
Nov 9 2022 at 11:33am
Sure, you can pretzel this into something no one cares about or claims, and then note how the uniformed “must suffer from cognitive limitation” because they don’t understand what an “economist or political scientist tells them” using “basic math.”
This above point was already made.
“If one voter controlled the votes” is a straw man. Using math gloss to prove the straw man is scientism. The math looks good but the point doesn’t.
Jose Pablo
Nov 10 2022 at 7:58am
Avalon, I don’t understand your answer but the belief that “in democracy I have a say” or “in democracy my vote counts” is one of the bedrocks of the system. This belief is key to the legitimacy of what Don Bodreaux refers to, in very fortunate expression, as the “high-school civics view of democracy”.
So, exposing this scam, as Pierre does here, is very relevant. No, in democracy you don’t have a say and your vote does not count in any meaningful way.
But it is even worse than that. I know intelligent people who believe that markets are tyrants because they don’t have a say on markets (they don’t count) while this very same people regard democracy as the ultimate expression of freedom because, in democracy, you know, they are “free to vote”
It is always worth to fight this widespread nonsensical misconception.
Avalon
Nov 11 2022 at 8:22pm
Pablo, I do understand what you have written. In your first sentence (re. “I have a say”) you are changing the argument. I don’t argue points I have not made.
I don’t believe voters in ordinary conversation/consideration distinguish count and counted in the way you assert, thus I dismiss it. It’s not the wedge you think it is.
“I know intelligent people who believe that markets are tyrants because they don’t have a say on markets …”
I too have objected to those views. That is not the point here and it is not a parallel.
“It is always worth to fight this widespread nonsensical misconception.”
Sure, if you are correct.
Like Gwartney et al wrote in their introductory econ text: “Most citizens recognize that their vote is unlikely to determine the outcome of an election.”
Pierre Lemieux
Nov 9 2022 at 12:21pm
Jose: Indeed, the difference in between “being counted” and “count.” If you set up to count to infinity, every number you add is being counted, but it doesn’t count because it doesn’t get you closer to infinity.
Pierre Lemieux
Nov 9 2022 at 12:27pm
Avalon: One may define terms as one wants. The criterion is whether the definitions are useful for analysis and understanding of reality. If one’s definitions lead to the conclusion that every elector decide who is elected, it is pretty clear that the definitions are useless. Otherwise, *I* could decide who gets elected. And it would be a deep mystery why any voter (not to talk about 1/3 of them) rejects the opportunity to decide who will rule over him.
Avalon
Nov 9 2022 at 1:47pm
“One may define terms as one wants. The criterion is whether the definitions are useful for analysis and understanding of reality. ”
Of course. The problem is your point doesn’t improve understanding of reality. Most people I talk to already understand their vote is one amongst very many, and the probability the election will be decided by one vote is vanishingly low. (And “felt” with zero formal math.) So the reality of why they bother to vote must lie elsewhere, whether the attached reasoning is sound or not.
“I am always surprised to find intelligent people who think that an ordinary voter, by using his single vote, has a significant chance of influencing the outcome \sout{and consequences} of an election.”
As an aside, I don’t accept vulgar sloganeering heard on TV and the like as “finding intelligent people…” or even that there is a clear and accepted meaning of the vulgarities.
So, I withhold believing you found that. Or maybe I doubt it is significant in any way, if such intelligent people do exist. Your findings “don’t count.”
Pierre Lemieux
Nov 9 2022 at 9:00pm
Avalon: There are parts of your comment that I don’t understand. But I should perhaps repeat what I think I have said before and should, it seems to me, be relatively clear from my post. My topic was why a rational individual does not vote in order to contribute to the victory of his preferred candidate or, in other votes, to make his vote count (“to elect my president”). My topic was not to explain what has sometimes been called “the paradox of voting,” which is, Why then do as much as two-thirds of individuals vote? I referred to this issue in the last two sentences of my (already too long) post, together with the citation of a book that those interested to pursue the topic may like to read; Brennan and Lomasky defend the expressive theory of voting, which is what my last sentence refers to. (The Mueller book is also useful.) Given my space constraints, I did not discuss the mystery of the Immaculate Conception either.
Avalon
Nov 11 2022 at 8:25pm
“But I should perhaps repeat … My topic was why a rational individual does not vote in order to contribute to the victory of his preferred candidate…”
That is not a repetition.
“There are parts of your comment that I don’t understand. … I did not discuss the mystery of the Immaculate Conception either.”
I have understood your writing.
Walter Donway
Nov 8 2022 at 9:34pm
The reason to vote is that I agree with the process my country has in place to decide which candidates, or ballot measures, the most citizens favor. I also agree that the candidate or measure receiving the most votes should prevail. And I agree that the more citizens who vote, the more credible is that process.
Therefore, I achieve my objectives nor matter who is elected or what is decided. And my contribution to achieving that objective is as meaningful as that of any other citizen who votes.
In other words, if I vote, then democracy wins by a slightly larger margin. And how important is it to me that democracy wins–i.e., sustains its credibility as my country’s chosen process. And because I know what life is like in nations what do not have democracy (a stipulation is that the democracy is a process for decision-making in a constitutional republic) I always win by voting.
In other words, no matter what the election or its outcome, my vote helps me get what I want, one of my highest priorities.
Today, in East Hampton’s high school, I achieved this objective (at a definitely leisurely pace) in about 10 minutes.
And in that 10 minutes, the agreement of my fellow citizens with the value of the process our efforts were achieving manifest in eager help, jokes, smiles, waves, and thank you from pretty women and jolly men working at the polls.
I submit to you that none of this stemmed in significant measure from concern with which candidate or which ballot measure prevailed. The good spirit arose from spending our time making real and effective a process–no matter what the outcome.
I hope you had a good time voting, too.
Jose Pablo
Nov 9 2022 at 9:56am
“I agree that the more citizens who vote, the more credible is that process”.
“In other words, if I vote, then democracy wins by a slightly larger margin”
These are also, very good reasons for not voting.
Walter Donway
Nov 9 2022 at 11:09am
I do not advocate a democracy. I advocate the democratic process within a limited constitutional republic, which greatly restricts the issues open to popular will.
Jose Pablo
Nov 9 2022 at 6:40pm
I certainly understand why is better that my behavior has as few “coercions” as possible open to any will other than mine.
But as far as a “coercion” remains “open”, I don’t see any difference between this coercion being open to “popular will” or to a “tyrant will”.
For instance: once I have to pay X amount of taxes I could not care less if this X amount has been decided by “popular will” or by the decree of a tyrant.
I am not fooled, even a bit, by the outrageous deception of saying that it is different because I get to vote to elect the representatives who define the tax code, and that my vote “counts”.
Pierre Lemieux
Nov 9 2022 at 12:50pm
Walter: Some elements of your substantial comment are interesting, but the issue is a bit more complicated that that. Otherwise, if only the process counts, inviting all citizens to participate in a fraternal round of smiling mini put or curling could do the trick. Conscription for a war against a common enemy, as nationalists sometimes wish for, would certainly do it. Another way to realize that things are more complicated is that you quite certainly don’t agree with the proposition that “the candidate or measure receiving the most votes should prevail,” for you would presumably not agree that a majority vote to abolish the 1st Amendment, or the 2nd, or the 4th, or the 5th should prevail. To get a better idea of what I am saying, may I recommend three short readings:
James Buchanan’s Why I, Too, Am Not a Conservative (or as a poor substitute, my short review of this short book);
My review of William Riker’s classic Liberalism Against Populism;
My review of two Francis Fukuyama’s books, which also relate to what is “constitutional democracy.”
Tiago
Nov 9 2022 at 12:39pm
I would go further than you. Not even the vote of very influential pundits matter.
“Gelman et al. also calculated that if a voter in New Mexico could have brought 5,000 of his fellow voters to switch from the other side to his, he would have had a 1.3% chance of flipping the state and a 1 chance in 6,000 of changing the nationally-elected president. ”
But even here, it is not your vote that makes a difference, but the persuasion. A person who did the persuasion and didn’t cast a vote would have the same effect.
Pierre Lemieux
Nov 9 2022 at 12:51pm
Tiago: Indeed, good point.
robc
Nov 9 2022 at 3:17pm
Results suggest my vote REALLY dont count.
And really, there is a reason to oppose grocery stores selling wine? Really?
The two Colorado ballot issues I cared about were a small* income tax cut (which passed easily) and the wine sales in grocery stores. The latter looks like it will fail despite my vote. It is close, so I guess it is possible my vote is going to count. I admit to not understanding how other people think, but that it didn’t pass in a landslide astounds me.
*4.55% to 4.40%.
Jens
Nov 9 2022 at 4:21pm
There are several strategies to bridge this apparent gap between low individual utility and collective relevance.
For example, one can combine local elections with supraregional ones. In the local election, the vote counts significantly more.
But there is also a good strategy to massively increase the benefit on the individual level: Rituals. People celebrate Christmas even if they are not Christians (anymore) and even if they are not children (anymore). You don’t have to do it in the ridiculous way of “celebrating democracy” when you vote, either. I would like to tell an example.
Where I live, votes are usually on Sundays (you don’t want to disturb people in usual workdays – the possibility of absentee voting has, of course, messed up the picture a bit). My father was not a particularly political person and we had very different views. He was also a victim of the neoliberal and free-market propaganda that was very widespread in the 80s and 90s, to which many people were mentally unequipped to respond reflectively at the time.
But he often went to play cards on Sundays, and if there was an election date at the same time, I was allowed to accompany him. Nothing special, really, but I can still remember many of those Sundays when we went to the polling station together and then to play cards. Always on foot, those were relaxed walks in which we had time to talk. I had the feeling of growing up.
Once I even argued with him in the voting booth about his voting decision, which earned me a joking admonishment from an election official. That wouldn’t even be possible today, because the procedures in the polling rooms have become much stricter, you’re not even allowed to take children who can already read into the voting booth – damn wokeness everywhere 🙂
Anyway. A simple ritual that made going to the voting booth a good experience for me as a kid, without even being allowed to cast a vote at all. My father didn’t do that consciously at all. He wasn’t much of a “democrat.” It was just a ritual that got introduced by accident. But just remembering these sundays today benefits for me.
And even though I now loathe the smoke-filled atmosphere of the card game, my sons go to the vote with me. Of course, you *can* make people hate what you hate by telling them it’s nonsense, implying negative feelings and dislike.
But it’s really no problem to make something else out of it. Anyone who has a hobby, or goes to church regularly, or has certain family rituals knows that. Making something individually useful and enjoyable out of the infinitesimally effective ballot, even on the family level, is no problem at all.
Craig
Nov 10 2022 at 9:51am
Actually wondering if the result in GA might change the minds of some libertarians, voting as libertarians? It looks like Oliver’s tally is about 2x the difference between Warnock and Walker. While a runoff complicates the mental calculation, the fact is libertarians are, at least mathematically, the difference in that race, as a group [which the Professor might find troubling!]. Would the result in GA make libertarians who post here more or less likely to vote, generally?
Pierre Lemieux
Nov 10 2022 at 11:29am
Craig: Of course, if you are a group with a 35,000 votes (the 1% between Warnock and Walker), by all means, get on you 70,000 feet, get your feet in your car, and go and vote your 35,000 votes. (Follow the Wikipedia link in my post: it will provide you with a better case.)
Pierre Lemieux
Nov 10 2022 at 12:15pm
Craig: Now, from a methodological-individualism perspective: as one of the 35,000, you know very well that had you voted differently (for Walker) or not voted at all, the outcome would have been indistinguishable from the current one. You see? that’s the problem.
Jose Pablo
Nov 10 2022 at 2:00pm
“You see? that’s the problem.”
That’s, certainly, one of the problems.
The other ones being:
a) You don’t know (as 90%+ of the voters) most of the policies that Walker stands for. You will base your vote on a few (or even one) sound bites or in the physical appearance of the candidate or, in this particular case, even worse.
b) You don’t know if the policies that Walker stands for now, are the same ones that he is going to support in the Senate
c) You have no clue if Walker’s support for these policies is going to “count” in the Senate. It is more likely that in the case of a general election, but far from guaranteed that Walker’s vote will be the deciding one in the Senate. And also, there are, fortunately, few things the Senate manage to decide by itself; for most policies the collusion of Congress, the Senate and the House, and the POTUS is required (God bless Gridlock!!)
d) And you have not even the most remote idea of how these policies, passed with the support of Mr Walker, if it is the case, and different from the ones he stand for during the campaign, are going to affect you as an individual if finally implemented (this is a tool, understanding how a given macro policy will affect us as individual, economist has not provided us with … yet).
Calling this “to have a say in political issues” is a total mockery.
vince
Nov 10 2022 at 10:59pm
Here’s a simple question: How does a candidate win an election?
Pierre Lemieux
Nov 12 2022 at 12:37pm
Vince: In all its extension, your question is very wide and covers a large part of public-choice theory. In the narrow limits of my post above, a politician wins an election (or an issue wins a referendum) by getting at least one vote more than the closest one (which, mind you, means different things in different vote-counting methods).
vince
Nov 13 2022 at 5:20pm
It’s one thing to make a recreational mathematical argument out of it, but do you really want to leave an election outcome to others, without your input? And it basically costs nothing to participate.
Pierre Lemieux
Dec 11 2022 at 11:43am
Vince: But that’s the point: a voter does not have any input with his single vote. Whether he votes or not, whether he votes for the candidate he most loves or he most hates, does not change the outcome of the election.
Matias Salimbene
Nov 13 2022 at 9:38am
In understand the reasoning but I still don’t get the point of this article.
I’ve seldom (if ever) find individuals thinking that their individual vote will steer an election result. But that doesn’t render the vote useless. The fact that so many people does go to vote, is what makes each individual vote less significant as a whole.
Then I read some of your replies, and sometimes you concede that the vote counts, or you are ambiguos about it. ¿So what then? I’m still not sure.
If you’re arguing that no single vote is relevant or influential, I agree. But a vote is never isolated and without context. And saying a single isolated vote is irrelevant, doesn’t mean that it doesn’t count. It just not what happens, each vote is counted.
Pierre Lemieux
Nov 13 2022 at 11:18am
Matias: An individual vote doesn’t count in the sense that the election outcome (and consequences) is the same if that individual had voted differently or not voted at all. I think I already said that, didn’t I.
See Jose Pablo’s post above where he points out that “count” and “be counted” don’t mean the same thing. Also look at my mathematical example in reply: infinity (at least on one dimension) is countable but adding one number on your way there doesn’t count. The risk of this example is, of course, that there is never an infinity of voter, so the probability of one decisive vote only tends to zero. But that’s enough to say that it practically doesn’t count. If you buy one more tomato per month, it does not practically increase the price of tomatoes: your individual action does not count as far as its collective outcome is concerned.
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