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What is the probability your vote will make a difference?

See here for more (including the link to the article by Nate Silver, Aaron Edlin, and myself describing what we did).



[Typo in caption to figure 1 fixed, thanks to commenters.]


  1. ljp says:

    Typo? I think that first sentence about Figure 1 should read "States with lighter colors…"

  2. Josh Myer says:

    Would it be more helpful to express the probabilities as a ratio against a "normal" vote? That is, instead of "1 in 10 million," it would be "30 times more likely to affect the result" (generously assuming 300M votes of equal weight).

    There's probably some weird normalization to worry about in determining the denominator, but it seems like a more approachable number for people below sigma+mu, if you catch my drift.

  3. Ed says:

    I think the caption under the first graph is wrong? Lighter colors signify decisive single votes, not darker colors?

  4. Alex F says:

    Typo in abstract: "probability you’re your" should of course be "probability your" (or, perhaps, "probability that your").

  5. DaveG says:

    What has happened since 2004?

    Why is Florida so far being looking important now?
    Would these plots have looked different then?

  6. Iain says:

    Log-probabilities might be clearer on the plot? I see other plots in the paper used log-probs. They were generally much more readable.

  7. Zubon says:

    DaveG, can you clarify that question? Florida is still in the top ten, and the question here is whether one vote in that state will be decisive. Florida is a big place, and the election there unlikely to be as close as in some recent years.

  8. Kevin says:

    So, if I'm more likely to die from lightning than have my vote matter, is it rational to vote?

    You probably won't die from voting, but look at it from a cost/benefits ratio. The cost is maybe an hour of your time. The expected benefit ( in terms of your vote making a difference) is extremely small. Why do so many people vote?

    Disclaimer: I have voted in some (but not all), presidential elections where I was eligible.

  9. Phil says:

    What's with the y-axis? At least make it read horizontally. And maybe label it "1 in 10 million", "1 in 20 million", etc.

  10. Zubon says:

    The expected benefit ( in terms of your vote making a difference) is extremely small. Why do so many people vote?

    Shall we skip the psychological and social reasons? The usual justification against a 1-in-10 million chance is that the benefits of having the right policies adopted are much larger. A 1-in-10 million chance at making a multi-billion dollar policy improvement is not a bad time investment. Granted, you do not capture much of that benefit, but we are being public spirited here.

  11. Andrew says:

    1. I did this plot without the log scale because I wanted to emphasize the absolute probabilities. For example, the difference between NM and NH is the same as between FL and zero. The log scale would spread out the bottom of the graph, but maybe we're not so interested in fine distinctions here. I have other plots on the log scale in the article; I figured people could take what they want out of these.

    2. Yeah, maybe labeling as "1 in 10 million" etc. would be better.

    3. I do think it's rational to vote in NM, VA, etc. In NY, where I live, it's more of a "civic duty" thing.

  12. Kaiser says:

    Is there a way to "invert" the scale? A nice way to present this data is to think in terms of the "effective" weight of one's vote. One-person, one-vote assumes each vote is equal weight but these probabilities show clearly that someone living in New Hampshire, New Mexico etc. has effectively more than 1 vote each while someone living in California, New York, etc. has effectively less than 1 vote each. Not all votes are created equal. I think this way of describing the data is more appealing.

  13. Michale says:


    You should be remember that social any psychological effects is the main issue for your vote.If there have any political crisis then it may influence at vote bank.


  14. Anonymous says:

    Who is Nate Silver ??

  15. daveG says:

    pls clarify-
    What has happened since 2004?
    Why is Florida so far being looking important now?
    Would these plots have looked different then?

    I guess I was thinking that it should be unlikely (even if top ten) that a state where the chance of a single vote being decisive is low should hold the balance.

    Of course it also depends on the actual propn of votes in each…


  16. William T says:

    I think that there is a fundamental fallacy in the assumptions underlying this analysis and the conclusion that "voting is not worthwhile". After thinking about it, it seems to me that the assumption that "a single vote could tip the balance" is actually not true. There are several reasons:

    1 – if the voting is very close, the result is certain to be challenged by recounts and lawsuits. These will almost certainly lead to votes being discarded for essentially random "defects". The result is likely to be determined by legal decision on admissibility of "defects" which affect large blocks.

    Therefore, an election result is not really "safe" unless the majority is significant. So your vote always makes a difference in proportion to that "margin of safety", not in proportion to a "singular majority".

    2. Cost of campaigning – this is inversely proportional to the margin of winning (historical and likely future). If you can construct a graph of "electoral cost" vs "margin of winning" then the contribution of each single vote in moving along that curve can be obtained. My guess is that it would be in the order of tens of dollars.