Participants 141
A given voting method can be classified as either Ordinal or Cardinal; these primary categories identify the type of information which is solicited from voters. That same method can also be secondarily classified as either a Direct-Score or an Iterative-Elimination method; these terms refer to the procedure employed to determine the winning candidate. There are lots of voting methods, some which fit into all four of the possible combinations of these two categories. We will define these terms and examine just a sampling of the many voting methods that have been proposed.
Ordinal methods – require voters to indicate the order of their preference for the candidates. A synonym for ordinal (which is more widely used) is Ranked-Choice Voting (RCV). Most ordinal methods require ranking at least the top two choices and very often it is three.
Some ordinal methods require a ranking of all the candidates, which is problematic from a practical standpoint. Many voters do not know enough about all the candidates to meaningfully rank them. There may also be write-in candidates about which most voters are likely to be unaware.
Another rather nasty problem with all ranked-choice methods is that they are unable to avoid the horrible blunder of sometimes electing a candidate that a majority of voters dislike (a real-world example was presented in the last lesson). The most obvious example is when, say, two or three candidates are running and voters do not like any of them; nevertheless, one of them will inevitably be elected.
Cardinal methods – ask voters to provide a numeric rating, grade or score for each candidate. Most cardinal methods use only positive scores (e.g. the 6 digits 0 through 5 or the scale of 0 to 100). Others allow both positive and negative scores (e.g. the 7 digits from -3 to +3).
Cardinal methods which utilize a “many valued” scale (e.g. a scale of 0 to 5 or 0 to 100) are highly vulnerable to an obvious strategic attack. Voters will quickly realize (in fact, it’s almost instinctive) that their ballot will have the most impact if they always award the candidate they like best the highest possible score and candidates they don’t like the lowest possible score. Intermediate values will be little used and the scores will not be dependably accurate measures of voters’ sincere opinions.
Cardinal methods that allow only zero or positive scores indicating how much each voter likes a candidate obviously can commit the same blunder of electing a candidate disliked by a majority of voters, just as all ordinal methods can. Also, the discussion in Lesson 8 about “preserving absolute zero” is relevant here.
Direct Score methods – simply compute a score for each candidate and crown the one with the highest score the winner.
Iterative Elimination methods – generally, compute a score for each candidate, then eliminate the candidate with the lowest score. After eliminating a candidate, some “adjustments” are usually made (that depend on the specific method) and the scores are recomputed. The remaining candidate with the lowest (recomputed) score is eliminated and the process repeats until only one candidate remains. The last remaining candidate is declared the winner. These methods obviously are more complicated to tally, but not necessarily much more complicated for voters. Such methods are often called “last man standing” methods.
The Perfect Voting Method – This hypothetical method (explained in Lesson 2) is a direct-score, cardinal method that uses a fine-grained, many-valued, negative-and-positive scale. It depends upon a fictitious “satometer” to extract sincere opinions from voters’ brains. In the real world (without a “satometer” or “truth serum”), its perfect performance would be considerably degraded by strategic voting.
There are some possible real-world ways to obtain more sincere scoring information from voters. However, that topic is beyond the scope of this course.
Plurality – is a direct-score ranked-choice method (voters are only allowed to rank their first choice). As previously explained, it is the most widely-used and the worst voting method.
Pairwise Comparison – is a direct-score, ranked-choice method. It was the method proposed by Condorcet in the late 1700s and is sometimes called the Condorcet method. It requires a complete ranking of all candidates by all voters. Condorcet’s idea was to compare every possible pairing of the candidates. If there is a candidate that a majority of voters ranks higher than every other candidate, it is declared the winner and is called a “Condorcet winner.”
Many people fell in love with Condorcet’s idea. Copious papers were written and many hypothetical election scenarios were analyzed. One much-discussed phenomenon is known as a Condorcet cycle. It is an election with candidates A, B and C where a majority favors A over B, B over C and C over A. This is often cited as an election “paradox.” Of course, it is not a paradox at all; it is just one of very many types of election with which voting methods must contend and still reliably identify the best candidate.
In addition to the problem of obtaining complete candidate rankings from all voters, Pairwise Comparison is an “incomplete” method. There are many elections in which a Condorcet winner does not exist, so Pairwise Comparison must be “supplemented” with another voting method which jumps in and handles all those cases. Frequently, the backup method is Instant Runoff Voting (explained below). Pairwise Comparison is in a lot of trouble with the Jones rule.
Borda Count – is another direct-score, ranked-choice method. It was the method proposed by Borda in the late 1700s. It, too, was based upon a complete ranking by all voters, but many variations of it have been proposed, most of which do not require complete rankings. Borda’s idea was to score the candidates on each ballot, add up the scores and deem the candidate with the highest score the winner. Points are awarded for the number of candidates the voter ranked below it. Specifically, in a race with N candidates, the top-ranked candidate on a ballot is awarded N – 1 points, the candidate ranked second, N – 2 points, the third, N – 3 points with the bottom ranked candidate always receiving N – N or 0 points.
Instant Runoff Voting (IRV) – is an iterative-elimination, ranked-choice method. IRV does not require complete rankings. Voters have the option of ranking up to their top (usually) three choices. Just the first choices are totaled for each candidate. If a candidate has a majority of the first choices, it is declared the winner. When no candidate has a majority, the candidate having the smallest number of first choices is eliminated. Any ballot which had the eliminated candidate as first choice will have its second choice (if any) promoted to first and its third choice (if any) promoted to second. The first choices are again summed for each candidate. If a remaining candidate now has a majority (of the remaining ballots), it is the winner; otherwise, the process is repeated until there is a winner.
People feel better that IRV winners always have a “majority” of votes, even though some “manipulations” may have been required to achieve that majority and some ballots may have been exhausted by that time. We also know that majority winners are not always the best choice. What is worse about IRV, is the fact that it can sometimes eliminate the candidate which should be the winner. However, allowing a second (and possibly third) choice which is promoted if the first choice is eliminated should greatly reduce the destructive pressure to vote insincerely for the “lesser evil.”
A few jurisdictions have replaced Plurality with IRV. However, so far, there does not appear to have been any obvious benefit.
Approval Voting (AV): — is a direct-score, cardinal method. Voters have the option of approving as many of the candidates as they like. Approval awards the candidate a score of 1. Lack of approval confers a score of 0. The scores are summed for each candidate and the candidate having the highest total is the winner. AV is the simplest cardinal method.
Because AV uses only a two-valued scale, it is immune to the strategic attack to which methods using many-valued scales are exposed. Any vote-for-the-lesser-evil pressure should be greatly ameliorated. At least there should be no disincentive for a voter to approve his true first choice, because it is still possible to also approve the “lesser evil.” However, approving the lesser evil will always help that candidate beat the voter’s true first choice.
STAR (Score Then Automatic Runoff): — is a direct-score hybrid cardinal/ordinal method. It first uses a cardinal (scoring) procedure to identify the top two candidates; then the ordinal information from the scoring is used to identify the final winner. Especially the scoring is vulnerable to strategic voting.
Approve/Approve/Disapprove Voting (AADV): — is a direct-score cardinal method. It may seem similar to AV, but actually is significantly different. Voters have the option of approving either one or two candidates. They also have the option to disapprove of one candidate. The scale has three values, -1, 0 and +1. An approval gives the candidate a score of 1, while disapproval confers a score of -1. Doing neither is a zero. The scores are summed and the candidate with the highest score wins. Note that a candidate’s disapprovals subtract from its approvals, so a candidate with more disapprovals than approvals would have a negative net score; there are some other important considerations as well. AADV will be discussed in more depth in a later lesson.
Best/Alternate/Worst Voting (BAWV): — is an iterative-elimination cardinal method. Voters have the option to identify up to three different candidates: the candidate the voter thinks is the best one; the candidate the voter thinks is the worst one; and an “alternate best” candidate. BAWV uses the same three-valued (-1, 0, +1) scale as AADV. A candidate marked “Best” receives +1; a candidate marked “Worst” is scored -1; a candidate marked “Alternate” is scored 0 as are all remaining candidates. The scores are summed for each candidate and the candidate having the lowest score is eliminated. For any ballot which had the eliminated candidate marked as best, the alternate choice (if any) is promoted to best and given a +1 score. The scores are again summed and the process is repeated until only one candidate (the winner) remains. BAWV is analyzed in-depth in a later lesson.
There are many more voting methods in the menagerie, some very complex. However, those described above should serve to illustrate the most important terminology and the large variety of proposed methods.
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