Philosophical Multicore

Sometimes controversial, sometimes fallacious, sometimes thought-provoking, and always fun.

Voting to Do the Most Good

Posted by Michael Dickens on August 4, 2012

If you are a United States citizen and you want to do as much good as possible with your vote, then how should you use it? (These principles apply outside the US as well, but my analysis focuses on US elections.)

Expected Value of Voting

For those who care about maximizing the welfare of society, the importance of voting increases as the population increases. Below is the mathematical justification for this claim. These calculations assume that you know the correct person to vote for. If you wish to avoid math, you can skip to the next section.

Let v = a number representing the expected value of voting.
Let n = the population size.
Let p = the proportion of the population that votes.
Let e = the expected value per person of your voting.
Let f = a number representing the opportunity cost of voting [1].

If v is greater than 0, voting is worthwhile. If v is less than 0, it is not.

If you only care about yourself,
v = e * (n*p choose n*p/2) – f

v is only greater than 0 for unrealistically large values of e or very small values of n.

If you care about every citizen,

v = n * e * (n*p choose n*p/2) – f

In this case, v increases as n increases; that is, the larger the population size, the more important it is that you vote.

Here, (n*p choose n*p/2) represents the probability that the vote will be exactly tied, as this is the only case in which your vote decides the election. This calculation assumes that everyone votes randomly between the top two candidates, which is incorrect but still works reasonably well as a model. The next sections attempt to refine this model.

The following sections assume that the voters must decide between two candidates. Most of the reasoning also applies to voting on a proposition.


If we know nothing about an election, we simply assume that the population is evenly split among options, in which case our vote has a relatively high chance of swinging the election. But we rarely know nothing about an election. Here I will continue to assume that the election is decided by popular vote, because the electoral college makes things much more complicated.

Let’s look at the 2008 election between Obama and McCain. Imagine that we are back in 2008, and it’s the day before the election. Gallup predicts that Obama will win with 55% of the popular vote, and McCain will receive 44%. Gallup has a history of effective representative sampling, so it’s safe to assume that this poll has no systematic bias.

Gallup’s sample size for this poll is 3050 participants. Remember, the only situation in which your vote changes the outcome is if the election is perfectly split 50/50. If the American population does indeed vote 50% for Obama and 50% for McCain, the probability of Gallup getting the results they did is about 1 in 3 billion (p = 3.0E-8). This significantly reduces the expected value of voting. I do not have the necessary knowledge of statistics to calculate the precise expected value in this case, but I would guess that voting is no longer worthwhile.

The Electoral College

The above calculations assume that we use a popular voting system—which is not always the cause. Under an electoral system, determining whether voting is worthwhile is much harder to figure out.

If you live in a district that consistently supports one party, then there is no point in voting if you are just interested in changing the outcome of the election (although this may not be the only reason to vote, as I discuss below). If, however, you live in a swing state, voting is a smart decision as long as both candidates are about equally favored (that is, the more-favored candidate has less than, say, 52% of the vote). Read the polls to determine whether voting is worth it.

Third Parties

In the United States, third parties have virtually no chance of winning a major election. But by voting for a third party candidate, you express your support for that candidate and platform. The more votes a third party gets, the more likely it is that at least one of the main two parties will adapt itself to move closer to the third party.

Suppose, for instance, the Libertarian candidate gets 5% of the vote. Republicans, who tend to agree with Libertarians on most points, know that they can win over some of those 5% if they change their platform to work better for Libertarians. When I vote for the Libertarian party, I express my support and increase the likelihood that Republican candidates will align their political positions more closely with those of Libertarians.

Furthermore, by voting Libertarian, I express my support to the public. If Libertarians get enough votes, mainstream voters (and especially swing voters) will start to take their opinions more seriously. It may influence more people to vote Libertarian or vote to support libertarian-minded policies within their own party of choice.

Which Party Is Best

I suspect that this section may be the most contentious of this essay. Many people believe that politics is a matter of opinion, and that I cannot tell you which party is best. I disagree. Questions about political policy are simply questions about which policy will best increase the welfare of beings in the world. Answering this question is not always straightforward. For instance, what sort of economic policy will best reduce unemployment? Such questions have empirical answers, but we don’t always know what they are.

Often, however, we do know which policy is best, and people only disagree because some sorts of biases—typically, old-fashioned and religiously-driven conceptions of morality—affect their thinking. For instance, abortion is clearly morally permissible for at least the first trimester and there is no legal or ethical reason to deny homosexuals the right to marry or at least form civil unions. If people didn’t base so much of their ethics on Christianity, which holds all human life as sacred and condemns homosexuality, this wouldn’t be a problem. (Other religions cause similar problems in other nations.)

Selfishness also causes a lot of political disagreement. People often desire their own happiness over the happiness of others, which causes many very wealthy people to oppose tax increases for the upper brackets (even though evidence suggests that, over a certain level of income, money has no effect on happiness). People also value the citizens of their own nation over the citizens of other nations, causing them to support foreign policies that hurt the citizens of other countries. Additionally, they value the present over the future, causing them to neglect long term problems such as environmental issues.

Democrats have better policies than Republicans on the majority of issues that have a clear right or wrong answer (e.g. abortion, gay rights, animal welfare, stem cell research, the existence of anthropogenic global warming, etc.) [2]. They disagree on a lot of issues that are much harder to judge, such as welfare, fiscal policy, and national defense spending. (If you have some way of objectively determining the best policy on one of these issues, by all means let me know.) But among those issues where the correct policy clearly follows from some basic tenets of morality, the Democrats have the advantage [3]. Given what information we have, the Democrats look like the party whose policies best improve the well-being of society.

But neither party effectively addresses the issues that matter most. Wild-animal suffering represents the biggest source of suffering we know of, but neither party cares even remotely about it [4]. The next three biggest issues are human mistreatment of non-human animals, human-caused environmental degradation, and impoverished humans in the developing world. Democrats tend to care more about these issues than Republicans, but neither party cares nearly as much as they should. It appears that the party that gives the most attention to these issues is the Green Party of the United States. It gives a great deal of attention to environmental issues. And in addition, it is the only national party that seriously addresses animal welfare in its platform:

Cruelty to animals is repugnant and criminal. The mark of a humane and civilized society lies in how we treat the least protected among us. To extend rights to other sentient living beings is our responsibility and a mark of our place among all of creation. We call for an intelligent, compassionate approach to the treatment of animals.

We reject the belief that our species is the center of creation, and that other life forms exist only for our use and enjoyment. Our species does not have the right to exploit and inflict violence on other creatures simply because we have the desire and power to do so. Our ethic upholds not only the value of biological diversity and the integrity and continuity of species, but also the value of individual lives and the interest of individual animals [my emphasis].

The bold section is critical. Many politicians accept the value of biodiversity, even if they do not push for policies to support it; but very few recognize that individual animals have interests that matter.

The Green Party platform not only proposes actions to reduce animal suffering, but also acknowledges the moral significance of animals and calls for an end to the homo sapiens-centric way of thinking that is the norm. This position is extremely important in that it helps cultivate people’s feelings of caring for animal suffering.

Which Party to Vote For

Although the Green Party appears to increase the general welfare more than any other party, this does not mean we should necessarily vote for them. Rather, we must consider the political climate of the United States, and try to put our vote where it will have the greatest positive impact.

If you have the chance to vote for a Green Party candidate who actually has a high probability of winning, then by all means do so. But in most elections, the Green Party nominee is a fringe candidate with little hope of victory. In such a case, it still makes sense to vote for him or her—as was discussed above.

We usually cannot do much good by voting in the primaries for the Green Party (GP). We ought to support the Green Party message rather than any particular candidate—as far as I can tell, no single GP candidate stands out as having far better policies than the others. We support the GP message by voting for them in the general election, but voting in their primaries does not do much good.

Instead, we should vote in either the Democratic or the Republican primary, depending on which is more strategically advantageous. You could vote for the mainstream candidate that you most support or for a candidate in the opposing party whom you expect to lose to your preferred candidate in the general election.

In the primaries, a vote does the most good in one of the mainstream parties; but in the general election, you should express support for your favorite candidate overall, irrespective of how few votes you expect them to get.

Local Elections

Local elections have low turnout (often around 5 to 10 percent), so your vote has a greater impact. Voting for a strong third-party candidate in a local election, even if she has little chance of winning, this will push her up in the ranks and cause her to be taken more seriously. Should she receive enough support, she may choose to campaign vigorously during the next election season and may even win. Your vote has a relatively high chance of giving her the support she needs to make a serious local impact.

If anything, voting for third-party candidates in local elections is more important than in national elections. I think the best way to increase support for a party’s platform is to vote to support that party in local elections and try to get the party in control of certain districts. Once the party is considered mainstream in those districts, it can more easily spread its influence to other districts.

Is Voting Worthwhile?

It is unclear exactly how much good voting does, but donating to an efficient charity probably has a much bigger impact. If it takes you a half-hour to vote, and you had spent that time working instead, the money you would have earned likely could have done much more good than your vote.

Of course, it’s not always possible to get paid for just half an hour’s work. If you can find some way to do that, great. Otherwise, voting may still be a good idea because it would have a low opportunity cost.

It is definitely more worthwhile to vote in local elections, especially if you live in a district where you expect your third party candidate to be able to get some serious support. (A GP candidate probably has a much better chance in Berkeley than in Lubbock.)

In summary: Vote for a major party in the primaries and the best party in the general election. Don’t neglect local elections. Vote Green when possible and Democrat otherwise.


[1] When I refer to a thing’s “value”, I mean the extent to which it improves the well-being of individuals in the world. It may not be possible to strictly quantify the value or the opportunity cost of voting; even if it is possible, it is certainly not easy. But we can make estimations, which is sufficient to make this equation useful.

[2] Here I will briefly justify the claim that each of these issues has a clear right or wrong answer.

abortion: For about the first half of pregnancy, a fetus cannot suffer and cannot have interests. Therefore, we do not violate its interest when we kill it. Once the fetus develops the capacity to feel pain, abortion becomes more questionable, but I still think it is permissible. For a more in-depth explanation as to why, see Peter Singer’s Practical Ethics.

gay rights: Allowing homosexual couples to participate in society in the same ways as heterosexual couples makes them happy, and has never been demonstrated to have negative effects.

animal welfare: See Animal Suffering.

environmental issues: All scientific evidence points to the fact that human actions are having a significant negative impact on the environment, which will greatly harm both humans and other animals.

anthropogenic global warming: Scientists agree—global warming is real, we are causing it, and we need to act fast to prevent it.

stem cell research: The only argument against stem cell research (as far as I know) is that it violates the sanctity of human life, which is an unjustified position.

[3] The only exception I know of here is that Democrats often support government involvement on economic policy where most economists believe that free-market solutions work better. For example, most economists agree that school vouchers improve the quality of schooling, whereas many Democrats disagree.

Of course, Libertarians deviate even further from mainstream economic opinion. Nearly all economists support government stimulus in response to economic recession, a policy that most Libertarians tend to oppose. Furthermore, Ron Paul and his supporters advocate for the gold standard, but close to 100% of economists believe it will not increase price stability or employment.

In reality, it’s not as simple as “more government” or “less government,” and a party that simplifies it so much—as Libertarians often do—misses many important nuances.

[4] We do have plenty of laws about how to treat endangered species, but the intention here is to conserve biodiversity, not to promote the well-being of the animals. Such laws are either motivated by anthropocentrism (i.e. we need certain species to provide us with resources) or by the strange belief that biodiversity is inherently valuable.


One Response to “Voting to Do the Most Good”

  1. I’m going to nitpick over your initial utility equations, but I wanted to let you know that the rest of your essay was great stuff.

    1. The distinction about caring about only yourself versus every citizen equally is a false dilemma, so that means that neither equation will be the one that people use.
    2. The value of f will be different in each equation.
    3. If e is a variable of average value, then it’s not applicable in the self-interested calculation, because I’m looking at value to a particular person — me.
    4. Though you mention it later in your essay, your equation doesn’t mention utility from voting apart from the electoral outcome (showing support, attracting attention to your values, exercising civic virtue, etc.)

    I think this equation works regardless of the agent’s values:

    U(V) = expected net utility of deciding to vote
    P(e*) = expected probability of your vote being the deciding vote of the election
    U(e*) = expected net utility of your candidate winning
    U(e) = expected net utility from the action of voting, apart from the electoral outcome
    C(o) = expected net utility of highest utility option you forgo by voting via opportunity vost

    U(V) = P(e*)U(e*) + U(e)

    If U(V) > C(o), then vote.

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