# Multiply Pr(decisive vote) by 2, perhaps

After reading our article on the probability that your vote is decisive, James Fowler wrote:

Doesn’t this estimate ignore David Nickerson’s APSR paper that shows 60% of the effect of contact spreads to a second person in the household? If people are connected in networks that are correlated in preferences (e.g. most friends of Democrats are Democrats) and increase exponentially in network distance (we have many more friends of friends than friends), then one person’s vote affects many more than just one person…. And hence ties are not the only outcomes that make a person pivotal.

And an earlier paper I wrote with a conservative estimate of the multiplier that was based on a 10% effect transfer rather than a 60% effect transfer.

My reply: Sure, maybe you should multiply this number by 2 if you’re married and can persuade your spouse. Or maybe multiply by 100,000 if you’re Oprah.

## 8 thoughts on “Multiply Pr(decisive vote) by 2, perhaps”

1. But even a factor of 2 puts you outside the confidence interval of your estimate, no? And my conservative estimate was based on a 10% effect between friends, but Nickerson's piece shows that in two-person households it is 60%. Who knows what it is on average across all close social relationships, but work within the Framingham Heart Study on obesity, smoking, and happiness (due out in December at BMJ) shows that social network effects are not trivial and they spread from person to person to person, even beyond two person households. My hunch for voting is that we are talking on average the real effect is somewhere between one and two orders of magnitude.

I am not claiming that this is a solution to the paradox of turnout — 1 in 100,000 is still bad odds, and as you know from your work and my work on altruism there is probably another explanation for that.

However, when Nate Silver broadcasts to the world what the probability of affecting the election is, it seems like this social network multiplier effect should be an important caveat to mention. I think it's time we stopped clinging to the Robinson Crusoe model of political behavior….

2. Richard: We're assuming you already have a preference, you're just deciding whether to vote or not.

James: I'm confused by what you're saying. We don't have any confidence intervals in that paper. My point was that, sure, say it's 1 in 10 million or 2 in 10 million. I find it very implausible that my decision to vote will affect 100 people. Oprah, maybe, but not me. But, yeah, maybe my decision to write these articles (as opposed to my personal decision to vote) could have a larger effect.

3. I think you glossed over Richard's comments too quickly. And I think James's are nearly irrelevant….as are yours, Andrew! If I understand what you're trying to estimate, it's not "what is the probability that you can influence the election in any way whatsoever," it's "what is the probability that THE VOTE THAT YOU CAST will be decisive." This probability is no higher for Oprah than it is for anyone else in Illinois (or wherever it is that she votes).

4. Phil. All these questions are interesting: what's the effect on Pr(my candidate wins) of (1) me voting, (2) me voting and telling others about it, (3) Oprah telling people to vote. Our paper was about question 1 but Fowler's questions are interesting too.

5. Andrew — my bad on the confidence intervals — I misremembered the estimation model from Gelman, King, Boscardin (1998) for which I thought there were confidence intervals — instead, there was a range of outcomes for different states.

Andrew — I understand the skepticism about the effect size, but think about Joe the Plumber — who knew he would have such a big effect on others? There is a lottery in social networks that occasionally allows even the non-Oprahs of the world to initiate cascades of influence. But ultimately, the actual size is an empirical question….

Richard — that influence is not independent of your actual vote if you tend to be socially connected to people with similar views. Increasing turnout among your friends and family on average increases the extra votes your preferred candidate will get because we live in politically correlated social networks.

Phil — if you vote and the counterfactual is "what happens to the world if I decide not to vote?" then that DECISION may in fact have an effect on others. You are right that one could imagine other possibilities — e.g. one counterfactual might be "suppose I tell my wife I am going to vote and we drive together to the polls and then when I get there I decide not to vote." In that case, then yes, I suppose you could have a counterfactual in which the only thing that changes is the final act itself. But the data in Huckfeldt and Sprague and elsewhere suggest that people who decide to vote tend to make that decision in advance of the election and tend to share information about that decision with others and this has an effect on others' decisions as well. Nickerson's study shows this isn't some artifact of observational studies — there is a real experimental effect that can flow from person to person to person.

Let me repeat — I DO NOT think this solves the paradox of participation. But I do think it is relevant to think about these magnitudes in order to make an inference about what group size would make general participation evolutionarily rational. A factor of 2 or 100 won't matter much for a US Presidential election, but it could very well make a difference in an early human group's effort to hunt a large animal or to defend against an attack from a rival group. If we are still using the same neurological tools to process these decisions that evolved hundreds of thousands of years ago in small group society, then getting the magnitudes right may matter….

6. Sure, maybe you should multiply this number by 2 if you're married and can persuade your spouse

If I had the ability to make my spouse to do what I want, I can think of a hundred ways I'd use that power before I'd use it to tell her how to vote.

7. Ubs: The idea I had in mind was that someone would persuade his or spouse to vote. That is, you already know how she'll vote, but she hasn't decided whether to bother to go to the polls (or to fill out the ballot and mail it in, if that's an option).