Condorcet Methods

In particular, among the many preferential methods, there are those that determine a so-called Condorcet (“con-dor-say”) winner, which many propose, as I do as well, delivers an optimum democratic decision in a wide range of contexts:

“A Condorcet method is any election method that elects the candidate [who] would win by majority rule in all pairings against the other candidates, whenever one of the candidates has that property.

” “A candidate with that property is called a Condorcet winner (named for the 18th-century French mathematician and philosopher Marie Jean Antoine Nicolas Caritat, the Marquis de Condorcet, who championed such outcomes).

A Condorcet winner doesn’t always exist because majority preferences can be like rock/paper/scissors: for each candidate, there can be another that is preferred by some majority (this is known as Condorcet paradox)…

“Ramon Llull devised the earliest known Condorcet method in 1299. His method did not have voters express orders of preference; instead, it had a round of voting for each of the possible pairings of candidates… The winner was the alternative that won the most pairings.” — Condorcet Method, Wikipedia

Round-Robin Competition

If we imagine conducting elections between each candidate and each other candidate, pair by pair, the Condorcet winner will be the candidate (if any) who beats every other candidate in such head-to-head elections.

It’s a “round-robin” competition. Every candidate competes one-on-one against every other candidate to determine the outcome.

This approach is also, perhaps more descriptively, called Instant Round-Robin Voting (IRRV).

We don’t actually have to conduct separate elections for each pairwise combination of candidates, of course; we can do this simply by getting each voter to number the candidates on a single ballot according to his or her own preferences.

Preference Cycles

Preference Cycle 1

The noted “paradox” is that, while any individual voter expressing his or her own preferences (rock, paper, scissors) cannot create a preference cycle (rock, paper, scissors, rock…), different people often have different preferences (paper, scissors, rock), so that such cycles can arise once we consider all the ballots together.

Nevertheless, the proposition remains that for general elections and by-elections the candidate, if any, who wins against every other individual candidate, one on one, will be the choice most acceptable to the majority.

If a preference cycle in the results does happen this assertion becomes more problematic; for a preference cycle can mean that there isn’t any candidate who meets this requirement, and then how we break the cycle will affect the outcome.

When we do have a Condorcet winner and yet have a preference cycle involving other candidates, how we break the cycle only affects the relative rankings of those other candidates, not the overall winner.

Condorcet “Completion”

Preference Cycle 3

The various Condorcet methods differ mainly in how they resolve these situations, even including falling back to another system such as Instant-Runoff Voting (IRV), or even FPTP again to resolve them. None of these is as good as Ranked Pairs, in my view, but certainly none is worse than starting and ending with FPTP alone.

As long as the solution we choose is well defined and is seen to a reasonable person as fair we can pick any of these preference-cycle approaches, and still improve the democratic responsiveness of the vote well beyond the limits of FPTP alone.

Democratic Legitimacy

“We advocate a voting system known as the Condorcet method for elections between more than two candidates…

“This method allows voters to submit a list of their top choices, in order, rather than just a single choice. Believe it or not, there is a lot of controversy about how to pick a winner from ballots like this. The Condorcet method selects the candidate who would beat any other candidate if they were the only two in the race.

“This method is the only system that can allow multiple similar candidates in the same race without hurting or helping each other’s chances. However, the main concern about the Condorcet method is that it may not produce an undisputed winner. When it does, it’s hands-down the best voting system to use. When it doesn’t, a tie-breaking protocol is used, which has no guarantees to satisfy everyone’s sense of justice.

“The main reason for our data collection is to see whether the Condorcet method produces an undisputed winner in real life. This data confirms our hypothesis.

“In all of the different samples that we polled, the Condorcet method not only produced an undisputed winner but usually an entire undisputed order of all the candidates…” – http://www.princeton.edu/~cuff/voting/

It is worth noting that for an FPTP election that yields a majority winner this winner is the presumptive Condorcet winner as well, irrespective that there’s no opportunity to express other preferences. However, as noted, FPTP results can be expected to be skewed as people second-guess the outcome and vote according to whom they think has the best chance to win, as opposed to voting their sincere preferences, and remembering that the system itself discourages additional competition.

Next: Condorcet Completion — Ranked-Pairs

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