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Some Issues with Ranked Choice Voting

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Paul Cohen
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Joseph Jones, who commonly goes by JJ, is considering how to vote in an upcoming election to choose a new mayor. Seven candidates, A, B, C, D, E, F and G, will be on the ballot. JJ considers three of these candidates, E, F and G, to be equally good choices, unlike candidate A whom JJ considers to be an awful choice. JJ thinks candidate B would be a poor choice, though clearly not as

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bad a choice as A. JJ doesn't know enough about candidates C and D to comment on either one.

The election is to be held using ranked-choice voting and JJ feels quite comfortable with that voting system. He understands that he must submit a list of six or fewer candidates, arranged in order of his preference, starting with his favorite one. He is confident about the mechanics of voting this way, and though he does not quite comprehend the details of how the votes are tallied, he trusts it will give a fair and accurate accounting of the votes.

Unfortunately, JJ is simply stumped about which candidate to designate as his top choice. He prefers G to F because he agrees enthusiastically with G on gun rights. F has said nothing about guns, but JJ prefers F to E because of F's strong position on immigration. And he prefers E to G because of their positions on the minimum wage. All three candidates seem like equally good choices to JJ.

Since JJ doesn't know anything about C or D, he decides to take advantage of his right to simply leave them off his list. Only because he must choose someone, JJ decides to put G first on his list; E and F fall naturally into line.

JJ has learned that with ranked-choice voting you should avoid putting any of the candidates that you most dislike on your ordered list of candidates, so he knows to make sure A is not on his ordered list. These considerations lead him to describe his choices to be G, F, E, B. But notice that it could just as easily have been F, E, G, B or E, G, F, B; the choice was completely arbitrary. If there were 300 voters who felt the same as JJ, no doubt they would split their votes evenly among these three options, giving about 100 to putting each one in first place. JJ does recall that the spoiler effect happens because of such vote splitting and that troubles him briefly, but that concern is quickly dismissed.

Unfortunately, JJ made a mistake in dropping off the two candidates C and D, a mistake that is compounded by including B at the end of his list. Including B but not C and D, his ballot would be interpreted as a vote for B during the last few rounds of tallying the ballots. Surely JJ did not want to support the election of B. He likely would have preferred to take a chance on one of the unknown candidates, C or D, rather than help B to be elected.

One lesson from this should be that ranked-choice voting has subtleties that could easily be unclear to some voters, maybe even most. But another is that ranking the candidates in order is not naturally so easy; in fact, it can be impossible without making unpleasant arbitrary choices. Such arbitrary choices are fodder for the spoiler effect and for erroneous election outcomes.

The claim that voters naturally and easily provide an ordered ranking of the candidates may seem very appealing, but it is simply untrue. Such an ordering will likely be artificial (see the comments for details on this), involving at it often must, the making of specious and arbitrary choices, merely to accommodate to this erroneous claim behind ranked-choice voting.

In contrast, if the election were held using balanced approval voting (BAV) then JJ would have surely indicated support for E, F and G and, much as with ranked-choice voting, JJ would have indicated no opinion regarding candidates C and D. The difference, though, is that with BAV, these no-opinion votes are tallied, as intended; with ranked-choice voting what JJ intended as a no-opinion vote is instead interpreted as opposition.

With BAV, JJ will vote opposition to A, but it is not clear how JJ will vote for B. As with ranked choice voting, JJ must make a choice. He could vote opposition to B, but he might instead specify neither support nor opposition; it all depends on how willing he is to take a chance on B winning election. But in contrast to ranked choice voting, with BAV that no-opinion vote does what JJ expects; it is interpreted as an expression of indifference about that candidate. It seems a good thing for a voting system to actually interpret votes in the way the voter intended.

However, with ranked-choice voting, while not listing a candidate may seem, to a voter, as a no -opinion vote but in the tally, it is interpreted as the vote of maximum opposition.

I should add that here, that I am taking some liberty with language. Ranked voting systems do not take account of either support or opposition; they deal only with relative positions. A voter who detests all the candidates might submit a ballot identical to another voter who thinks that any of the candidates would be a good choice. And that identical ballot might be submitted by a voter who favors only half of the candidates while not supporting the others.

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Attended college thanks to the generous state support of education in 1960's America. Earned a Ph.D. in mathematics at the University of Illinois followed by post doctoral research positions at the Institute for Advanced Study in Princeton. (more...)
 

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2 people are discussing this page, with 5 comments  Post Comment


Paul Cohen

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Ranked choice voting pre-supposes that voters are able, without much effort, to simply list the candidates in an election in what mathematicians call a linear order. In fact, this is the most constrained type of order system that mathematicians commonly discuss.

A linear order is a special kind of tree (a tree with only a trunk and no branches), and in turn, a tree is a special kind of partial order. The weakest (and so the most common) kind of ordering is a partial order. But as noted in the Wikipedia reference, even a partial order must be reflexive, transitive, and antisymmetric.

In the JJ example, we can easily find that G

Submitted on Saturday, Mar 29, 2025 at 4:49:59 PM

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William WAUGH

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Reply to Paul Cohen:   New Content

Your comment appears as cut off in the midddle. It becomes somewhat more readable when someone tries to reply to it. But there are odd characters, as though maybe you composed it on Microsoft Word and then the coding of it didn't get translated properly.

Submitted on Saturday, Mar 29, 2025 at 5:40:28 PM

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Paul Cohen

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Reply to William WAUGH:   New Content

I've not looked at it but that was something I worried about. The symbol was supposed to be a "less-than or equal" symbol. Thanks for pointing that out; and yes I did compose with Word.

Submitted on Saturday, Mar 29, 2025 at 6:33:32 PM

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Paul Cohen

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I'll try this again, replacing the offending character with the offending character replaced by

Ranked choice voting pre-supposes that voters are able, without much effort, to simply list the candidates in an election in what mathematicians call a linear order. In fact, this is the most constrained type of order system that mathematicians commonly discuss.

A linear order is a special kind of tree (a tree with only a trunk and no branches), and in turn, a tree is a special kind of partial order. The weakest (and so the most common) kind of ordering is a partial order. But as noted in the Wikipedia reference, even a partial order must be reflexive, transitive, and antisymmetric.

In the JJ example, we can easily find that G

Ranked choice voting (when there are several candidates) assumes an improbable structure for voter preferences; this would rarely be the case. But ranked-choice voting requires voters to impose a linear order for their ballot, and voters comply, usually by introducing arbitrary decisions and perhaps even falsehoods. The resulting information collected in the election will be contaminated with various forced errors. Often these will be claims of non-existent preferences, but some may even be counter-factual. However, in tallying the ballots the erroneous claims are indistinguishable from the true ones. Both must be treated with the same seriousness.

Submitted on Saturday, Mar 29, 2025 at 6:48:50 PM

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I agree that requiring strict ranking causes problems. Some ranking systems have been proposed that allow equal ranking (e. g. Ranked Robin). But I think hybrid rating-ranking systems would be fairest (can't prove it, though).

Submitted on Saturday, Mar 29, 2025 at 5:43:44 PM

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