Runoff Voting Systems
Ordinary runoff voting systems require voters to come back to polls for one or more rounds of voting.
The standard Plurality Plus Runoff (or Plurality Runoff or Two-Round) voting system works as follows:
(a) Voters come to the polls and each voter votes for one candidate.
(b) If one candidate wins a majority of votes cast, that candidate is elected.
(c) Otherwise there is a second round election (a “straight fight”) between the candidate who won the most votes (but less than a majority) and the candidate who won the second most votes. This requires voters must come back to the polls a second time.
Such runoff elections are quite common. As we saw, French Presidential elections are run this way. Usually week or two elapses between the first and second round of voting.
A potential and more elaborate type of runoff voting system is the Multi-Round type, which would work as follow.
(a) Voters come to the polls and each voter votes for one candidate.
(b) If one candidate wins a majority of votes cast, that candidate is elected.
(c) Otherwise the candidate with the fewest votes is eliminated and a runoff election held among the surviving candidates.
(d) The process of eliminating the candidate with the fewest votes and holding another runoff among the survivors some candidate receives a majority of the votes cast (which must occur once all candidates but have been eliminated and there is a “straight fight” between just two surviving candidates).
This more elaborate type of runoff is impractical to use in elections because it would require voters to come back to the polls many times. (The 2002 French Presidential election had 16 candidates, so voters probably would have had to make 15 trips to the polls.)
Instant Runoff Voting (IRV) has recently received considerable attention. Its appeal is that it “simulates” runoff elections but does not require voters to come to the polls more than once. Instead voters come to the polls once and provide complete information about their preferences over all the candidates on a single ballot on which they rank the candidates in order of preference. These ordinal ballots then can be counted so as to simulate runoff elections or either the ordinary or more elaborate type.
The ordinary variant of IRV works as follows:
(a) Voters come to the polls and each voter ranks all the candidates on the ballot in order of preference.
(b) If one candidate is ranked first by a majority of voters, that candidate is elected.
(c) Otherwise there is a simulated runoff between the candidate the candidate with the most first preference ballots and the candidate with second most first preference ballots. This is accomplished by transferring the ballots on which eliminated candidates were ranked first to one or other of the surviving candidates on the basis of second or lower preferences on those ballots.
(d) The surviving candidate with the majority of (first preference plus transferred) ballots is elected.
In parallel manner, the more elaborate version of IRV simulates a sequence of runoffs as one candidate at a time is eliminated. Note that the more elaborate type of IRV is as practical to use in elections as the ordinary version because, in either event, voters never make more than one trip to the polls. In fact, the more elaborate version of IRV has been used in Australian, where it is known as the Alternative Vote.
The distinction between the ordinary and more elaborate versions of (instant or non-instant) runoff elections is consequential, since they can produce different winners from the same preference/ballot data (e.g., the same preference profile).
In principle (e.g., in the simplified voting situations in Problem Set #2), each IRV variant produces the same winner as its ordinary runoff counterpart. But in practice, this probably will not be true because, in ordinary runoff elections, turnout may go up down in different rounds of voting and/or voters may change their preferences over candidates between rounds of voting.