Plurality voting is simple, and theoretically provides incentives for voters to compromise for centrist candidates rather than throw away their votes on candidates who can't win. Opponents to plurality voting point out that voters often vote for the lesser of evils because they heard on the news that those two are the only two with a chance of winning, not necessarily because those two are the two good compromise candidates. This gives the media significant election powers. Condorcet runs each candidate against the other head to head, so that voters elect the candidate who would win the most sincere runoffs, instead of the one they thought they had to vote for.
There are circumstances, as in the examples above, when both instant-runoff voting and the 'first-past-the-post' plurality system wouldn't elect the Condorcet winner. (In fact, FPTP can elect the Condorcet loser and IRV can elect the second-worst candidate, who would lose to every candidate except the Condorcet loser.) When there is a Condorcet winner that IRV doesn't elect, a majority would by definition prefer the Condorcet Winner to the IRV winner. Supporters of the Condorcet criterion see it as an important criterion when choosing a voting method. They see the Condorcet criterion as a natural extension of majority rule. Condorcet methods tend to encourage the selection of broadly supported candidates who appeal to the median voter. Here is an example that is designed to support IRV while making Condorcet look bad:
499 A>B>C
3 B>C>A
498 C>B>A
B is preferred by a 501–499 majority to A, and by a 502–498 majority to C. So, according to the Condorcet criterion, B should win, despite the fact that very few voters rank B in first place. By contrast, IRV elects C and plurality elects A. The goal of a ranked voting system is for voters to be able to vote sincerely and trust the system to protect their intent.
The importance of this scenario, of two parties with strong support, and the one with weak support being the Condorcet winner, may be less than one would expect, though, as it is common in plurality voting systems (see Duverger's law), but much less likely to occur in Condorcet or IRV elections, which unlike Plurality voting, punish candidates who are opposed by a significant block of voters.
Here is an example that is designed to support Condorcet while making IRV look bad:
33 A>B>C
16 B>A>C
16 B>C>A
35 C>B>A
B would win against either A or C by more than a 65–35 margin in a one-on-one election, but IRV eliminates B first, leaving a contest between the more "polar" candidates, A and C. Proponents of plurality voting state that their system is simpler than any other and more easily understood.
All three systems are susceptible to tactical voting, but the types of strategy used and how often there is value in voting strategically differ in each method.
Like all voting methods, Condorcet methods are vulnerable to compromising. That is, voters can help avoid the election of a less-preferred candidate by insincerely (strategically) raising the position of a more-preferred candidate on their ballot. However, Condorcet methods are only vulnerable to compromising when there is a majority rule cycle, or when one can be created.
All Condorcet methods are at least somewhat vulnerable to burying. That is, voters can sometimes help a more-preferred candidate by strategically lowering the ranking of a less-preferred candidate on their ballot.
Scholars of electoral systems often compare them using mathematically defined voting system criteria. The criteria which Condorcet methods satisfy vary from one Condorcet method to another. However, the Condorcet criterion implies the majority criterion, and thus is incompatible with independence of irrelevant alternatives (though it implies a weaker analagous form of the criterion: when there is a Condorcet winner, losing candidates can drop out of the election without changing the result), later-no-harm, the participation criterion, and the consistency criterion.
Condorcet methods are not known to be currently in use in government elections anywhere in the world, but a Condorcet method known as Nanson's method was used in city elections in the U.S. town of Marquette, Michigan in the 1920s, and today Condorcet methods are used by a number of private organizations. Organizations which currently use some variant of the Condorcet method are:
Smith set
In voting systems, the Smith set, named after John H. Smith, but also known as the top cycle, or as Generalized Top-Choice Assumption (GETCHA), is the smallest non-empty set of candidates in an election such that more voters prefer any candidate in the set over any candidate not in the set in head-to-head matchups. The Smith set is one way to determine who the best candidates in an election are. Voting systems that always elect a candidate from the Smith set pass the Smith criterion and are said to be "Smith-efficient".
A set of candidates where every candidate in the set pairwise beats every candidate not in the set is known as a dominating set.
The Smith set can be calculated with the Floyd–Warshall algorithm in time Θformula_1. It can also be calculated using a version of Kosaraju's algorithm or Tarjan's algorithm in time Θformula_2.
It can also be found by ordering the candidates by their number of pairwise victories minus pairwise defeats (a Copeland method ranking), and then looking for the smallest group of candidates, starting from the top, who pairwise beat all candidates not already in the group.
Example using the Copeland ranking:
A pairwise loses to C, so it is certain that all candidates from A through C (A, B, and C) are in the Smith set. However, there is one matchup where a candidate who is known to be in the Smith set loses or ties someone who may or may not be in the Smith set: C loses to D; so D is confirmed to be in the Smith set. Another such matchup can now be seen: D ties with E. So E is added into the Smith set. Because all of A through E beat all candidates other than each other, the Smith set is A through E.
Tomás Carlovich
Tomás Felipe Carlovich (20 April 1949 – 8 May 2020) was an Argentine professional football player and coach. He was born in Rosario, Argentina. As a coach, he managed Central Córdoba. As a player, he played for Rosario Central, Central Córdoba and Independiente Rivadavia.
On 6 May 2020, Carlovich was beaten with a shovel by a robber in Rosario while riding his bike. He died two days later in a coma at a hospital from his injuries, aged 71.
Cécile Rol-Tanguy
Cécile Rol-Tanguy (10 April 1919 – 8 May 2020) was a French communist. She was a Resistance fighter during World War II. She was active in the liberation of Paris. She was secretariat and a liaison officer, in charge of operations and confidential communications. She was born in Royan, Saintonge.
In 2008, Rol-Tanguy became the Grand Officer of the Legion d’Honneur.
Rol-Tanguy died at her home in Monteaux, Loir-et-Cher on 8 May 2020, aged 101.
Pairwise comparison
Pairwise comparison is any process of comparing things in pairs to judge which of two things is preferred, or has a greater amount of some something, or whether or not the two things are identical. The method of pairwise comparison is used in the scientific study of preferences, attitudes, voting systems, social choice, public choice, requirements engineering and multiagent AI systems. In psychology literature, it is often referred to as paired comparison.
If someone shows what they like more between two options, this preference can be expressed as a pairwise comparison. If the two alternatives are "x" and "y", these three pairwise comparisons are possible:
The person prefers "x" over "y": ""x" > "y"" or ""xPy""
The person prefers "y" over "x": ""y" > "x"" or ""yPx""
The person has no preference between both alternatives: ""x" = "y"" or ""xIy""