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Publications and source records attributed to Richard B. Darlington.
For decades the minimax voting system was well known to experts on voting systems but was not widely considered to be one of the best systems. But in recent years two important experts, Nicolaus Tideman and Andrew Myers, have both recognized minimax as one of the best systems. I agree with that. This paper presents my own reasons for preferring minimax. The paper explicitly discusses about 20 systems.
In a single winner election with several candidates and ranked choice or rating scale ballots, a Condorcet winner is one who wins all their two way races by majority rule or MR. A voting system has Condorcet consistency or CC if it names any Condorcet winner the winner. Many voting systems lack CC, but a three step line of reasoning is used here to show why it is necessary. In step 1 we show that we can dismiss all the electoral criteria which conflict with CC. In step 2 we point out that CC follows almost automatically if we can agree that MR is the only acceptable system for elections with two candidates. In step 3 we make that argument for MR. This argument itself has three parts. First, in races with two candidates, the only well known alternatives to MR can sometimes name as winner a candidate who is preferred over their opponent by only one voter, with all others preferring the opponent. That is unacceptable. Second, those same systems are also extremely susceptible to strategic insincere voting. Third, in simulation studies using spatial models with two candidates, the best known alternative to MR picks the best or most centrist candidate significantly less often than MR does.
The electoral criterion of independence of irrelevant alternatives, or IIA, states that a voting system is unacceptable if it would choose a different winner if votes were recounted after one of the losers had dropped out. But IIA confuses the candidate who withdrew with the data which was generated by that candidate. This paper reports a wide variety of simulation studies which consistently show that data from dropout candidates can be very useful in choosing the best of the remaining candidates. These studies use well-validated spatial models in which the most centrist candidates are considered to be the best candidates. Thus IIA should be abandoned. The majority judgment or MJ voting system was created specifically to satisfy IIA. Some of these studies also show the substantial inferiority of MJ to other voting systems. Discussions of IIA have usually treated dropouts as strictly hypothetical, but our conclusions about the usefulness of dropout data may apply even to real dropouts.
When each voter rates or ranks several candidates for a single office, a strong Condorcet winner (SCW) is one who beats all others in two-way races. Among 21 electoral systems examined, 18 will sometimes make candidate X the winner even if thousands of voters would need to change their votes to make X a SCW while another candidate Y could become a SCW with only one such change. Analysis supports the intuitive conclusion that these 18 systems are unacceptable. The well-known minimax system survives this test. It fails 10 others, but there are good reasons to ignore all 10. Minimax-T adds a new tie-breaker. It surpasses competing systems on a combination of simplicity, transparency, voter privacy, input flexibility, resistance to strategic voting, and rarity of ties. It allows write-ins, machine counting except for write-ins, voters who don't rate or rank every candidate, and tied ratings or ranks. Eleven computer simulation studies used 6 different definitions (one at a time) of the best candidate, and found that minimax-T always soundly beat all other tested systems at picking that candidate. A new maximum-likelihood electoral system named CMO is the theoretically optimum system under reasonable conditions, but is too complex for use in real-world elections. In computer simulations, minimax and minimax-T nearly always pick the same winners as CMO.