No voting system is perfect. Each makes different tradeoffs between various properties. Given the wide range of possible voting systems, it can be fruitful to study theoretical properties of different voting systems to try to determine which ones will have more desirable properties in the widest range of cases.
The distinguished economists Partha Dasgupta and Eric Maskin have a working paper that offers immensely important insights into the theoretical properties of various voting systems. Entitled “Elections and Strategic Voting: Condorcet and Borda“, the paper considers several voting methods and investigates their theoretical properties. The main contribution compared to previous election theory literature is a focus on which systems incentivize strategic voting by citizens. This is important because if a system encourages strategic voting, it places a large burden on citizens to figure out how others might vote in order to cast a ballot that will give the highest chace to the outcome they most prefer. A voting system that encourages strategic voting seems exceedingly undesirable.
The authors analyze voting systems that include the following examples:
- Plurality rule, also known as first-past-the-post, where voters choose one candidate and the candidate with the most votes wins the election.
- Runoff voting, where there are two rounds. In the first round, each citizen votes for one candidate. If some candidate wins over 50% of the vote, they win; if not, the top two vote-getters advance to a runoff.
- Majority rule, also know as a Condorcet system, where each voter ranks the candidates in order of preference. The winner is the candidate who beats all other candidates in head-to-head matches based on the rankings.
- Rank-order voting, also known as the Borda count, where voters again rank the candidates. But this time, each ballot allocates points to the candidates depending on the ranking. With n candidates, a candidate gets n points for each first choice, (n-1) points for each second choice, and so on. The winner is the candidate with the most points.
- Approval voting, where each voter approves as many candidates as they want. The winner is the candidate with the most approvals.
- Range voting, where voters score each candidate on a scale, for example a ten point scale where 10 means “superb” and 1 means “dreadful”. The points for each candidate are summed across all ballots, and the winner is the candidate with the most points.
With so many ways of setting up a voting system, how is a society to select which method to use?
Dasgupta and Maskin take the approach of setting out several axioms that are desirable in a voting system. They then investigate which voting systems satisfy the greatest number of those axioms in the widest range of cases. Most of the axioms are standard in the literature, but the two most important in this study are (1) strategy-proofness and (2) no vulnerability to vote-splitting. Strategy-proofness in this context means that a voting rule should induce citizens to vote according to their preferences, not to vote strategically. No vulnerability to vote splitting is called the independence of irrelevant alternatives (IIA) axiom in the paper. Vote splitting arises when candidate x would beat candidate y in a head-to-head contest, but loses to y when z runs too (because z split off some votes that would have otherwise gone to x). A voting rule that satisfies that IIA axiom will not be vulnerable to vote splitting.
These two axioms seem highly desirable for any voting system to satisfy. And if you agree they are desirable, then you will be interested to know Dasgupta and Maskin’s finding: if a voting systems satisfies the set of desirable axioms, then it must be majority rule, i.e. the Condorcet method. As the authors put it: “We show that, among all voting rules, majority rule is uniquely characterized by strategy-proofness, the Pareto principle, anonymity, neutrality, independence of irrelevant alternatives, and decisiveness.”
This striking result needs to be considered alongside two important remarks.
First, the instant-runoff voting (IRV) system that is often called “ranked choice voting” is not the same as majority rule. Although IRV involves ranking, it falls most closely to the “runoff voting” terminology in the examples given above. This system does not satisfy some very desirable axioms, including that instant-runoff voting is vulnerable to vote splitting (in the terminology of the paper, it violates the IIA axiom). Such vote-splitting occurred during the 2022 Alaska special election for the U.S. House of Representatives seat, and our blog previously discussed Jeanne Clelland’s excellent analysis of that race.
The second important remark is that some popular voting methods like approval voting and range voting, while having some desirable properties, suffer from not satisfying strategy-proofness. In other words, based on the Dasgupta and Maskin model, those systems incentivize citizens to vote strategically.
To illustrate the strategic voting, consider an approval voting election with three candidates: x, y, and z. Suppose there are 100 voters, and each voter has some utility from each option winning the contest. Each voter also has a threshold value where if the utility from an option is above the threshold, they mark approve, and otherwise the voter does not approve that option on the ballot. Suppose that if each voter cast a ballot following their preferences, the outcome was:
| Candidate | Approvals |
| x | 40 |
| y | 30 |
| z | 30 |
Now consider 11 of the voters that had the preference y > z > x. Suppose these voters receive 10 utility if y wins, 5 utility if z wins, and 1 utility if x wins. Also, suppose their threshold for approval was 6, so that in this election, they only marked approval for candidate y. Well, if these 11 voters mis-represented their true preferences, and gave an approval mark to candidate z, then the outcome would change to z winning the election, and those voters are better off. Thus, approval voting incentivized strategic voting in this case. A similarly simple example can show that range voting also suffers from incentivizing strategic voting.
Final takeaway
The upshot of this study for me is that majority rule or “Condorcet’s method” has highly desirable theoretical properties. Of course, empirical evidence about voting system performance will also be important. But this theoretical result is crisp enough that it lends further promise that tweaking IRV to make it a Condorcet method, like the Bottom-Two Runoff IRV method does, would be a great direction for election reform advocates to take.