The risk of Tied Elections

By Warren D. Smith & Clay Shentrup

Tied and near-tied elections cause crises that undermine governments.

An example: Panama's presidential election of 1948. Arnulfo Arias Madrid won by 1562 votes – although the supreme court had not decided whether he was even eligible to run. But then after clashes in the streets, Arias Madrid fled to the Canal Zone and Domingo Diaz Arosemana was declared victor after 2714 Arias votes from Veraguas were declared invalid. But Diaz died in office in 1949. After that, the National Election Jury declared Arias Madrid the true winner, retroactively reversing its earlier decision and kicking out Diaz's VP. But then Arias Madrid was impeached. In the original election, conducted via plurality voting, there were many political parties and it is entirely unclear to me who "should" have won the 1948 election, because nobody knows what all the voters for third-party candidates wanted.
And in Costa Rica in the same year 1948, a disputed election led to a civil war; same thing happened in Nigeria 1965.

Obviously, with 0-99 range voting, a tie at the top is about 100 times less likely than with plurality voting.

But switching from plurality to IRV voting would instead significantly increase the risk of ties since one could occur every single round. Unlike, say, a tie between the 4th and 5th-place finishers in range voting, which does not matter since it does not affect the identity of the winner, in IRV every tie matters because every one, even ties between apparent "no hopers" with below 1% of the vote can affect the identity of the winner. Combine this with the other nightmarish logistical properties of IRV and you get a disaster waiting to happen.

Computer simulation I

In a 10-round IRV election, you might naively guess there is 10 times larger tie-risk than in a plurality election. Actually it is worse than that because the early rounds are more likely to have ties – but it is better than that because usually, the way that early-round ties are resolved does not affect the final outcome (although in principle they always can). In the computer simulations in paper #95 here, 1247400 elections (each with three candidates and either 23 or 24 voters) produced these numbers of ties where an IRV first-round-tie has been counted as a "tie" even if its resolution did not affect the identity of the winner. (Readers who do not like that presumably should mentally decrease the IRV tie count to about 75% of the value we give.)

Voting system #tied
Range 8029
Plurality 60750
IRV 158355

Of course, a lot of ties happened in this computer study because there were only 23 or 24 voters, and a lot fewer would happen with 1000 times more voters. However, the relative proportions of these tie counts should stay roughly the same with more voters.

Computer simulation II

See these pictures and note the prevalence of "random dotty" regions (indicating "near-tie nightmares") in the IRV pictures.

What if there are only two voters, both honest?

It is fairly common in real life that two people have to make a collective decision among several possible choices. (This situation is an extreme case, hence good as a test.)

Now, obviously, practically every ranked-choice voting method (and plurality voting too) is usually going to yield a perfect tie, and then some coin-flipping is going to be called for. (For example, I say go to a pizza place for dinner, you say Chinese. Result: tie.) You can try instant runoff voting or Condorcet, but you are still usually going to get a tie and the method is going to work poorly, even with 100% honest voting.

For example, if the coin-flip says "Chinese" that might be a disaster since one of the voters is allergic to MSG, hates Chinese food, etc. Her views get totally ignored with probability 50%.

With honest range voting (especially using a continuum range such as the real interval [0,1]) ties are uncommon – we usually get a unique best choice and nobody's views are ignored. (Borda also works pretty well with two honest voters.)

A useful mental example

Here's an interesting hypothetical election to keep in mind when considering the risk of ties under IRV (Instant Runoff Voting).

%Voters Their vote
50 Kiss > Miller > Curley
25 Curley > Miller > Kiss
25 Miller > Curley > Kiss

With plain plurality voting, Kiss wins in a landslide and there's no recount called for.

With IRV Miller and Curley are nearly tied, and so all kinds of recount lawsuit nonsense ensues. Then the winner of that battle goes against Kiss, and then he and Kiss are nearly tied and so another series of lawsuits ensues. Recently, for example after the nearly-tied Franken-vs-Coleman senate race in Minnesota 2007 which was replete with lawsuits, IRV shills such as at "FairVote" have been distributing propaganda of the form "if only we'd had Instant Runoff Voting, this nightmare near-tie+lawsuit scenario would not have happened in Minnesota." That's true (vote transfers from Independence Party candidate Dean Barkley, who got over 400,000 votes, would have, almost certainly, broken the tie, probably giving Franken a lead on the order of 20,000 votes over Coleman). But what the IRV shills forgot to say is that IRV also leads to ties and near-tie elections, and overall in more cases than plain plurality voting, as well as potentially leading to worse nightmares which are harder to resolve. So IRV actually is worse as far as tie-risk and nightmare-risk is concerned, and the IRV shills' propaganda to Minnesotans was exactly wrong.

A recent election that would have led to a nightmare with IRV

Logic isn't good enough? Computer simulations aren't good enough? OK, here is a recent important real election to consider if you want to know how bad IRV could get:

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