Related to: Shut up and multiply, Politics is the mind-killer, Pascal's Mugging, The two party swindle, The American system and misleading labels, Policy Tug-of-War

Jane is a connoisseur of imported cheeses and Homo Economicus in good standing, using a causal decision theory that two-boxes on Newcomb's problem. Unfortunately for her, the politically well-organized dairy farmers in her country have managed to get an initiative for increased dairy tariffs on the ballot, which will cost her $20,000. Should she take an hour to vote against the initiative on election day?

She estimates that she has a 1 in 1,000,000 chance of casting the deciding vote, for an expected value of $0.02 from improved policy. However, while Jane may be willing to give her two cents on the subject, the opportunity cost of her time far exceeds the policy benefit, and so it seems she has no reason to vote.

Jane's dilemma is just the standard Paradox of Voting in political science and public choice theory. Voters may still engage in expressive voting to affiliate with certain groups or to signal traits insofar as politics is not about policy, but the instrumental rationality of voting to bring about selfishly preferred policy outcomes starts to look dubious. Thus many of those who say that we rationally ought to vote in hopes of affecting policy focus on altruistic preferences: faced with a tiny probability of casting a decisive vote, but large impacts on enormous numbers of people in the event that we are decisive, we should shut up and multiply, voting if the expected value of benefit to others sufficiently exceeds the cost to ourselves.

Meanwhile, at the Experimental Philosophy blog, Eric Schwitzgebel reports that philosophers overwhelmingly rate voting as very morally good (on a scale of 1 to 9), with voting placing right around donating 10% of one's income to charity. He offers the following explanation:

Now is it just crazy to say that voting is as morally good as giving 10% of one's income to charity? That was my first reaction. Giving that much to charity seems uncommon to me and highly admirable, while voting... yeah, it's good to do, of course, but not that good. One thought, however -- adapted from Derek Parfit -- gives me pause about that easy assessment. In the U.S. 2008 Presidential election, I'd have said the world would be in the ballpark of $10 trillion better off with one of the candidates than the other. (Just consider the financial and human costs at stake in the Iraq war and the U.S. bank bailouts, for starters.) Although my vote, being only one of about 100,000,000 cast, probably had only about a 1/100,000,000 chance of tilting the election, multiplying that tiny probability by a round trillion leaves a $10,000 expected public benefit from my voting -- not so far from 10% of my salary.

Of course, that calculation is incredibly problematic in any number of ways. I don't stand behind it, but it helps loosen the grip of my previous intuition that of course it's morally better to donate 10% to charity than to vote.

[Disclaimer: the above $10 trillion estimate is not mine. Bush did not kill 10 billion current people (at $1,000 per life) and he massively increased health-oriented foreign aid to Africa, which can expiate many sins in the GWWC calculus. Politics is the mind-killer, this is not about blue and green, etc.] So we have a model of politics as charity, on which it is more plausible that voting on policy could be rational. But why stop there? If voting (wisely) is a charitable activity, then spending money on political contributions to convince or mobilize others to vote (wisely) could be as well. For those who don't have moral objections to politics as charity (see the comments in this discussion for examples of such objections) political influence affect the voting behavior of others can be as well (provided compared to spending on tuberculosis treatment. We can attempt to remedy or analyze the "incredibly problematic" components to make better and better estimates. When thinking about effective philanthropy, would the marginal dollar do more good as a political campaign contribution or as a charitable donation for tuberculosis treatment?

Politics as effective charity?

This is not a new question for those interested in optimizing the impact of their charity. Giving What We Can (GWWC), founded by Future of Humanity Institute associate Toby Ord, is a group of people who have pledged to give at least ten percent of their incomes "to whichever organizations can most effectively use it to fight poverty in developing countries." GWWC notes that political advocacy may have high expected value, but has not recommended any organizations in that category, mentioning the difficulties of analysis as well as hope that it will be done in the future.

While those who care about future generations and existential risk might not choose to focus their charitable efforts on the task of GWWC, thinking about how political activity relates to it can still provide them a good example for a Fermi calculation. For instance, charity evaluator GiveWell, which posts its analysis online, estimates the cost of saving the life of a poor person alive today via their recommended charities as on the order of $3,000, giving a reasonably clear benchmark for political activity to exceed.

This post and its successors will lay some further groundwork for that Fermi calculation.

Are votes worth buying?

To make the comparison between political activity and GiveWell-style anti-poverty organizations as clear as possible we focus solely on money spent to convince or mobilize the votes of others (as opposed to one's own vote, which may be easy enough to exercise to be worthwhile, even if efforts to influence others are not).

We can then break up the initial analysis into three parts.

How much political spending is required to elicit a vote for a candidate under various conditions?
What is the relationship between purchased votes and policy outcomes?
What is our probability distribution over the value (in lives of the poor saved, for this example) of those policies?

We could then delve deeper into questions of decision theory, value, signaling and bias that are raised by the basic empirical picture. Today's post will focus on the first prong, the cost per vote elicited via political spending (in the context of a two-boxing decision theory, for the moment).

How much do votes sell for?

To begin the analysis, we can consider as our example contests for the most powerful elected office today: President of the United States. Three lines of American evidence stand out as relevant to assessing the cost per vote of campaign spending: the revealed behavior of politicians, correlational studies of spending and electoral outcomes, and experimental evidence from randomized trials. The first and third indicate relatively low cost per vote, while the second suggests higher costs. For the causal judgments we wish to draw, randomized experiments offer the most powerful evidence, and this analysis will lean heavily on them.

Revealed preference

In the United States, politicians dedicate an enormous proportion of their time to fundraising. Prima facie, this suggests that politicians, experts in getting elected, believe that fundraising will be at least as helpful to their election as other activities like personal appearances or actual governance. This is made more plausible by the tendency of politicians to spend more time fundraising and raise more money when facing serious challengers in their next election. Politicians might have been tricked by an initial baseless belief in the efficacy of campaign spending, with the most popular candidates also raising the most money and creating a spurious self-fulfilling correlation. However, selection over time would be expected to wear away at such mistaken beliefs.

Correlation studies

A number of correlational studies have been cited to advance the idea that 'campaigns don't matter' in U.S. presidential elections. Using information such as party identification, unemployment, economic growth, and the approval rating of the incumbent, political scientists can predict election outcomes surprisingly well before campaigning even begins. These correlations are only weak evidence of causation, however, since the fundamentals also predict fundraising capacity (more popular candidates do better at raising money from the public, and organized interests are more interested in buying influence with a candidate who looks likely to win). To be confident that additional spending will buy votes, one would ideally want robust randomized experiments capable of clearly indicating causal relationships.

Randomized experiments

Fortunately, the last several decades have seen a proliferation of randomized experiments and scientific methods in political campaigning. In these experiments, parties and political organizations randomly apply particular campaigning methods, often with the supervision of political scientists or other academics, and record the votes thus secured. One reference is Donald Green and Alan Gerber's Get Out the Vote, which reviews dozens of experiments bearing on the cost-effectiveness of get-out-the-vote (GOTV) efforts.

The key results are summarized in a table on page 139 (viewable on the Google Books preview). The strongest well-confirmed effect is for door-to-door GOTV drives, which average 14 voters contacted to induce one vote (plus spillover effects), with a cost per vote of $29 (including spillover effects) assuming that staff time costs $16/hour for staff. Phone banks require more contacts per vote, but are cheaper per contact, with Green and Gerber estimating the cost per vote at $38 for campaign volunteer callers, and $90 for untrained commercial callers.

In recent years, the U.S. political parties have adjusted their GOTV strategy in line with these experiments, and turnout has increased. For instance, in 2004 Green and Gerber predicted predicted that the parties would increase GOTV spending by some $200 million using methods averaging $50 per vote, for an increase in turnout of 4 million, and the turnout data seems consistent with that. This money was concentrated in swing states, and in 2004 turnout increased 9% to 63% in the twelve most competitive states, while increasing 2% to 53% in the twelve least competitive states (while clearly leaving many potential voters home).

However, publication biases likely inflate the cost-effectiveness estimates here, perhaps drastically, and to get a solid (likely worse) estimate would require a detailed investigation of such biases. Many of these studies are weakly significant, inconsistent across circumstances, or involve degrees of freedom. The true cost per vote could easily be $1,000+.

Diminishing returns

But how finely targeted can GOTV efforts be? Adding n votes to both candidates in a two-candidate race is a disappointing result for those interested in affecting who wins in elections. A GOTV which mobilizes 1000 votes at the margin, but has 250 of them go to the non-preferred candidate, will be only half as effective as one that solely mobilized supporters of the preferred candidate. Fortunately for electoral campaigners, the candidate citizens will vote for (if mobilized) is often easy to determine. Voting behavior is highly predictable from rural vs urban location, ethnicity, age, past party registration, neighborhood, etc. With increasing spending on GOTV, increasingly less selected populations would need to be contacted. Depending on how much money is available (and accompanying diminishing returns as less polarized populations are approached) this might easily double or triple the cost per vote at the margin.

A further problem is that, since the forecast likelihood of a vote making the difference in an election varies widely across the country, other donors will also apply their resources disproportionately to closely contested elections. For instance, Gelman et al find that a U.S. presidential election vote in New Hampshire is around a hundred times as likely to make a difference as one in California. National presidential campaigns can efficiently allocate their resources in order of priority, with additional dollars going to relatively marginal regions. In non-national elections candidates may call in favors and tap war chests to deal with particularly close races, and empirical data do indicate increased spending in tight races. We can sanity-check an estimate of the cost per vote against total spending by national campaigns, e.g. the 2008 U.S. presidential race:

Candidate (Party)	Amount raised	Amount spent	Votes	Average spent per vote
Barack Obama (D)	$532,946,511	$513,557,218	69,498,215	$7.39
John McCain (R)	$379,006,485	$346,666,422	59,948,240	$5.78
Ralph Nader (I)	$4,496,180	$4,187,628	738,720	$5.67
Bob Barr (L)	$1,383,681	$1,345,202	523,713	$2.57
Chuck Baldwin (C)	$261,673	$234,309	199,437	$1.17
Cynthia McKinney (G)	$240,130	$238,968	161,680	$1.48
Excludes spending by independent expenditure concerns. Source: Federal Election Commission[1]

These amounts are surprisingly small (relative to, e.g. the U.S. federal budget), and also include all non-GOTV interventions. Negative campaigning which reduces turnout for an opposing candidate is just as effective in winning elections (per vote) as increasing turnout for one's preferred side. Interventions which push 'swing voters' to vote for one candidate rather than the other are twice as effective as either per voter influenced.

Some ballpark VOI guesstimates

Much more analysis can obviously be done here, but as a first-pass estimate, it seems likely that the marginal cost per vote from spending on U.S. presidential general elections is higher than the $50 per vote Green and Gerber estimate for GOTV efforts, so consider a range of $50-$5000. Note that these are after-tax dollars if contributed directly to political campaigns, and non-profit efforts are constrained in their ability to back particular candidates and coordinate with their campaigns (although many activities can be funneled through non-profit vehicles).

What would that be worth? For those considering how to spend their effectiveness-focused philanthropy budget, we could use Eric's quick guesstimate of a 1 in 100,000,000 probability of a marginal vote swaying a presidential election. But if we consider ex ante close elections the number might be one in tens of millions (if one holds one's donations for close elections, although Gelman's figure of 1 in 10 million was for a specific election, using polls from immediately prior to election day, exaggerating the degree of certainty). Say we take 1 in 25 million as our number, assuming one waits for close elections to donate, but can't wait until just before election day.

Then in order for campaign spending to outperform the Against Malaria Foundation saving one child from death by malaria for ~$3,000+, the victory of the preferred candidate would need to be expected (given extensive uncertainty about candidates' future behavior, future conditions, and the effectiveness of various policies) to do good equivalent to preventing over 400 thousand to over 40 million extra malaria deaths, with higher numbers more likely.

With higher estimates of the campaign spending cost per vote, political donations would look less attractive, but voting oneself has potentially lower cost, the opportunity cost of reliably informing oneself (an essential cost) and voting. So carefully voting oneself might be useful volunteering, even if political donations are not worthwhile in this framework. One might think of it as spending a gift of political power from the state.

Continued in: Probability and Politics