Presumably in a large sample (here being cases, not people), some will be statistical ties and some not. For example, the senate is in a statistical tie, as is Pennsylvania and Brazil, and many others, but the house isn’t, nor is Montana, etc., etc. We tend to notice statistically tied races (and settings) because they are where swings happen, so they are important but a statistical tie seems so unlikely that having one would seem unstable, yet they seem to persist for long periods (e.g., most swing states remain swing states for many elections). Is there some force keeping these pencils balanced in their points, or is this merely a perceptual selection bias?

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    By statistical ties, are you referring to races where the spread in opinion polls is less than the margin of error? For example, 49% to 47% with a margin of 3%, others being undecided.
    – Rick Smith
    Commented Oct 31, 2022 at 14:45
  • They are ties, because they became ties at some point and no major change happened.
    – whoisit
    Commented Oct 31, 2022 at 15:13
  • It looks more like OP is concerned with a 50-50 split in a voting body with an even number of voting candidates.
    – hszmv
    Commented Oct 31, 2022 at 15:44
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    Be careful when applying statistics to non-random actors. For example, in the US "winner take all" two-party system, all you need is 50% + 1; why should a national political party invest more in a particular race, resources they can use elsewhere, than it takes to push them comfortably over the line? If a race is close, both parties may push large resources towards that race trying to get over that line resulting in a very close race. Conversely, they'll avoid putting resources into locations they don't think they can win.
    – Schwern
    Commented Oct 31, 2022 at 16:56
  • &whoisit: But because there is so much focus on these ties, you'd think that there would be lots of chaos, and so lots of reason for major change. @schwern: I guess I'm asking (per &rick_smith's interpretation, and maybe &hszmv's too -- although I'm not sure these differ), with all the money going into these, and 50/50 being a tipping point, and so probably chaotic, how do they manage to not tip? [It only let's me "@" one person, so I've pseudo-@'ed everyone else via &. Sorry.) Commented Oct 31, 2022 at 18:43

1 Answer 1


There does seem to be a lot of close elections, don't there? But this is partially an example of selection bias, partially the nature of politics (and the U.S. system in particular), and partially the limitation of polling:

Limitations of polling: There is no widely agreed upon meaning of "statistical tie," and actual pollsters and statisticians don't really like the term. The media typically use to mean it falls within a poll's margin of error. But that means a 49%-43% result with a 3.1% MoE is actually a "statistical tie," even though in all likelihood candidate A is beating candidate B rather soundly. And unsurprisingly, media outlets like to take every opportunity to portray a race as closer than it is to keep people tuned in.

Selection bias: You mention that the U.S. Senate and the Pennsylvania Senate races are tight, while the House is not. But the U.S. House election is really 435 distinct elections, and the Senate election is around 30. RealClearPolitics indicates that only seven of the Senate races this year are toss-ups as of this writing, and only 33 of the House races. What that really means is there are four hundred or so races where the results are not close at all. Naturally, neither the media nor politicians focus on the races that are foregone conclusions.

Nature of politics: Parties and politicians are rational actors who want to maximize their chances of winning elections. In the U.S. in particular, most candidates run in a first-past-the-post, winner-take-all system. That means there is no benefit to coming in a respectable second and you pretty much have to shoot for 51% of the vote (or 51% in 51% of the districts) to gain power.

This highly incentives a two-party system and moderation towards the mean voter. That in turn tends to naturally result in races that are deadlocked as both parties are entering a contested race with the candidate, platform, and messaging they believe gets them closest to 51%.

If both parties were pouring their resources into Pennsylvania and the polling was 60%-40%, that's a sign someone horribly miscalculated. And hey, that does happen. But the game never stops gets played and parties can correct their mistakes in later rounds. The U.S. is now in Round 118, and the players have gotten pretty good at it.

  • Thank you for the detailed analysis. I slightly misdirected the discussion with mention of statistical ties. The thing that confuses me isn't that there are statistical ties at per-election level, which you've well explained (and I'd guess that it was largely selection bias), but, to put the question a different, specific, way: Why the senate, which, as you point out, represents 100 separate elections, has been nearly 50/50 over a very long period of time. Most of those are nowhere near 50/50, so why do 100 of them seem to always hover around 50/50? Is it mere coin flipping? Commented Nov 1, 2022 at 4:03
  • @jackisquizzical while these are separate elections, they are linked by the fact that there are only two competing actors with finite resources. If the actors are rational, they would figure out which events are "certain" (i.e. resources needed to win them would be disproportionate to their role in overall result for the currently-losing side) and focus on "uncertain" ones - "coin tosses" or close to it. As both sides would, presumably, thus commit to same events - assuming equal resources and amount of "certain" events for both sides, overall result would thus become close to 50-50 split. Commented Nov 1, 2022 at 9:15
  • It's basically a feedback loop, right? When things get out of balance, the party out of power makes more of an effort to recover.
    – Barmar
    Commented Nov 1, 2022 at 14:08
  • I’m not sure these explanations work in this case. The populations of the solid heads and tails are essentially immovable regardless of $ spent. Why are there the same number of immovable heads as tails? Commented Nov 1, 2022 at 14:16
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    @Barmar: Also a significant chunk of the electorate likes a split in government, getting politicians bogged down in campaigning and filibustering rather than being able to rapidly change the rules. Uncertainty in law has a cost above and beyond the long-term effect of the new law.
    – Ben Voigt
    Commented Nov 1, 2022 at 15:08

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