Thanks to HS Mathematics teacher, David Harvey for this explanation!
A voting method is a procedure by which we take the preference lists of individual voters (i.e., a ranking of the candidates) and generate from them a preferred choice (i.e., a winner). Any such procedure is call a social choice function, and the field of social choice theory concerns itself with the strengths and weaknesses of various procedures.
What mathematical properties make a voting system good?
There are many mathematical properties that are desirable for any voting system, such as:
- A voting method should always produce a winner (Always-a-Winner Criterion).
- A voting method should pick as the winner the candidate who would beat every other candidate in head-to-head contests (Condorcet Criterion).
- If a voting method picks candidate A as the winner, then if voters had put candidate A even higher up in their preference lists, candidate A should still have won (Monotonicity).
- If a voting method picks candidate A over candidate B, then adding another candidate C in the election without changing any voter preference relative to A to B, A should still beat B (Independence of Irrelevant Alternatives).
However, mathematics also reveals...
- Mathematics reveals that NO voting system exists that has all these properties. The type of theorem that demonstrates this is an example of an "impossibility theorem." As a result, the electorate must choose which elements are most desirable (or undesirable) and choose a method accordingly. For instance, the method we use currently for electing a president -- plurality voting -- does not have the second property listed above (think Bush, Gore, Nader election) and ranked choice voting does not have the second, third, or fourth properties.
What then are the benefits of ranked choice voting (RCV) over our current system when there are more than two candidates?
There are other properties, some non-mathematical, that do make RCV desirable, such as:
- RCV has been shown to be relatively resistant to strategic manipulation (people voting strategically rahter than according to their true preferences in order to improve the likelihood of their preferred candidate winning.)
- RCV allows voters to more fully express their preferences.
- RCV leaves less impetus for negative campaigning than plurality voting as candidates also get value in being the second or third, etc. choice on voters' ballots.
- RCV requires only a single ballot, as opposed to a run-off system where the top two candidates (neither of whom won more than 50% of the vote) face each other in a separate second round vote.
- RCV is simple enough that the electorate can understand the system, use it properly and trust its results.
Are other states using ranked choice voting?
The upcoming 2021 NYC primaries will use RCV for the first time. Sixteen other states have adopted RCV for upcoming local elections, and Maine was the first state to use RCV for a presidential election in 2020.
FairVote. (2021). Ranked choice voting. FairVote.org. https://www.fairvote.org/ranked_choice_voting
Taylor, A.D., & Pacelli, A.M. (2008). Mathematics and politics: Strategy, voting, power, and proof (2nd ed.). New York, NY: Springer.