Data for Vote Decisions in a City Council Election

Tempe Arizona residents were recently sent mail ballots for the city council election of March 12, 2024. Three of the five candidates on the ballot are to be elected to the council. A voter may vote for up to three candidates, and the three candidates with the highest vote totals are elected.

Suppose a voter can quantify her preferences on a scale of 0 to 10, with 10 meaning she definitely wants the candidate on the council and 0 meaning she definitely does not want the candidate on the council. For example, her preferences might be as follows:

Candidate Utility

A 10

B 9

C 3

D 1

E 0

She can vote for one, two, or three candidates. Clearly, she should not vote for candidate E, whom she does not want on the council under any circumstances. But what about the other candidates? Suppose she decides to vote for candidates A and B, her highest ranked candidates. Should she vote only for those two, or should she also use her third allowed vote for candidate C? Voting for C might prevent one of the least preferred candidates, D or E, from being elected. On the other hand, what if voting for C pushes C’s vote total ahead of either A or B? Then the voter’s support for C could knock one of her preferred candidates out of the running.

Her optimal choice, according to the large body of scientific literature on strategic voting, depends on what is known about the chances of each candidate winning the election — in other words, on knowledge of what other voters plan to do. Strategic voting methods aim to maximize the voter’s total utility by combining the voter’s utility scores with the voter’s expectations of the election outcomes.*

For a multiple-seat election, Laslier and van der Straeten (2016) prescribed ranking the candidates by their expected vote totals. In our example, the candidate expected to have the most votes is ranked 1 and the candidate expected to have the fewest votes is ranked 5. Suppose that before the election, the voter thinks that the following results are likely:

Expected rank Candidate Utility Utility difference from main contender

1 E 0 –10

2 B 9 –1

3 D 1 –9

4 A 10 9

5 C 3 2

For each candidate, calculate the difference in utility between the candidate and the candidate’s main contender. For candidates ranked 1 to 3, who are considered likely to win, the main contender is the strongest expected loser, the candidate ranked fourth. For candidates ranked 4 and 5, who are considered likely to lose, the main contender is the weakest expected winner, the candidate ranked third. For example, candidate E, who is considered likely to win, is compared with fourth-ranked candidate A, and the utility difference is (0 – 10). Candidate A, who is considered likely to lose, is compared with the weakest expected winner candidate D, with utility difference (10 – 1).

The strategic voter then selects the (up to) three candidates with the highest utility differences, limiting the selection to the candidates whose utility difference is positive. For our example, this means voting for candidates A and C, but not for second-choice candidate B. Under the strategic voting system, the voter assumes that B will win anyway and uses her ballot to help candidates A and C, who would need her vote to win.

There are two problems with this voting strategy. First, it seems somewhat dishonest to vote something other than one’s preference (the literature calls this insincere voting). Second, what if the voter’s expectations of the election results are wrong? If the data are flawed, or if enough other people with the same preferences follow this same strategy, candidate B will lose even though the voter prefers B to C, D, and E.

We rarely have perfect information about what will happen in an election. There are no polls for the Tempe city council race; even if there were polls, they would likely have a low response rate and would not necessarily predict the election results. There is, however, some information available from past elections that might be relevant to the 2024 election.

Figure 1 shows the vote percentage for each candidate in the previous four city council races by incumbency status. Each election was held to fill three seats, and all incumbents won. On average, incumbents had about a 7 to 8 percentage point advantage over non-incumbents. That might lead the voter to think that incumbents would get more votes, on average, than non-incumbents.

Figure 1. Percentage of votes for incumbents and non-incumbents in previous Tempe City Council elections.

The other piece of information comes from candidates’ financial statements, available for all but two candidates for 2020 and 2022 from https://cityoftempeaz.easyvotecampaignfinance.com/home/publicfilings. Figure 2 shows the relationship between the vote percentage and the total receipts to date from the January 15 filing preceding the election. There are few data points, but in each election winning candidates had raised more money than the losing candidates.

Figure 2. Percentage of votes attained vs. amount of money raised as of January 15 before the election. Points for the 2022 election are black, and points for the 2020 election are blue. Two candidates (one from each year) were missing financial information; these candidates had the lowest vote totals.

With this information, what should our voter do? Recognizing the limited amount of information about other voters’ intentions, she could simulate outcomes under a range of scenarios. A voter with the preferences expressed at the beginning of this post should vote for her highly desired candidates A and B. The decision on candidate C then depends on how likely other candidates are to win. If A and B are highly likely to win (e.g. they are incumbents with high fundraising, or there are other reasons to believe they are likely to win) then voting for candidate C might prevent one of the less desirable candidates D or E from winning. If D or E is likely to win, then she should not vote for candidate C because that vote might cause C to defeat candidate A or B.

Note that our voter’s decision would be easier if Tempe used ranked choice voting, Borda count, or another method that allows voters to express more detailed preferences. With ranked choice voting, she would simply rank candidates A through E from 1 to 5 in decreasing order of preference on her ballot, and would not need to conjecture about what other voters plan to do. If her first-choice candidate A is eliminated in the first round of tabulation as having no mathematical chance of meeting the required vote threshold, then her second-choice candidate is considered and so on until all candidates are chosen.** See https://vote.minneapolismn.gov/ranked-choice-voting/ for how the city of Minneapolis uses ranked choice voting for municipal elections.

Footnotes and References

*Myerson and Weber (1993) assumed that each voter wishes to maximize her expected utility and prescribed the following procedure for an election with one winner. For each pair of candidates i and j, the voter estimates the probability p(i,j) that those two candidates would be tied for first place. The prospective rating of candidate i equals the sum of p(i,j) [u(i) – u(j)] over all other candidates j, where u(j) is the utility of candidate j, and the strategic voter then selects the candidate with the highest prospective rating.

**Ballot tabulation is done iteratively until all seats are filled. For a three-seat election, the first tally counts the first-choice candidates on all the ballots. Candidates receiving more than 25% of the first-choice votes (25% of the votes plus one) are elected. If fewer than three candidates are elected after the first tally, then the counting continues. Candidates with no mathematical chance of winning are eliminated; ballots that list an eliminated candidate as first choice then have their second-choice candidate considered. Thus, if candidate A is eliminated in the first round of counting, our voter’s second-choice candidate moves up to first choice. If candidate A is elected in the first round of counting, the surplus votes for candidate A are allocated proportionally to the second-choice candidates on those ballots so that no votes are wasted.

Laslier, Jean-François, and Van der Straeten, Karine (2016). Strategic voting in multi-winner elections with approval balloting: A theory for large electorates. Social Choice and Welfare 47 (3): 559–87.

Myerson, Roger and Weber, Robert (1993). A theory of voting equilibria. American Political Science Review 87: 102-114.