A voting method is the critical mechanism at the heart of an election that performs the function of gathering some specific information from each voter and then processing it in some manner to select the “best” candidate(s) in each race. There are hundreds of different voting methods. The simplest is named plurality—or, as it is sometimes called, first past the post.
Plurality asks each voter to indicate which of the candidates is the best. It allows each voter to vote only for one candidate. Plurality processes that data simply by separately adding up the number of voters who selected each candidate. The candidate indicated as best by the most voters is deemed the winner. Note that in a four-candidate race, the winner could have been chosen as the best by as few as 26% of the voters.
Not only is plurality the simplest voting method, but it is also the most widely used. It may be the only voting method most people know; some probably think it is the only voting method. Unfortunately, plurality is also the worst of all voting methods. It does the worst job of consistently picking the winner with which the voters, as a group, would be most satisfied. The use of plurality is the most important single reason why elections have always worked poorly right from the beginning.
Plurality’s Many Problems
Around the time of the American Revolution, two French scholars, Nicolas de Condorcet and Jean-Charles de Borda, pointed out some of the serious problems with plurality. They proposed voting methods of their own that they theorized were superior. This kicked off a 240-year-long debate over various alternative voting methods. More recently, it has been realized that plurality is even worse than Condorcet and Borda thought.
Plurality is a main cause of the divisive polarization we suffer (Duverger’s Law). Plurality can even force voters to elect a candidate that the majority of voters actually oppose! As an actual example, polling data just ahead of the 2016 presidential election clearly revealed that a majority of the voters disliked both Trump and Clinton. Yet Trump was nevertheless elected. The same thing happened in 2020 when clear majorities disliked both Trump and Biden, but Biden won anyway.
Why ever would voters elect a candidate that the majority of them oppose? They do so because plurality allows each voter to vote only in favor of one candidate, so the majority of voters voted (insincerely or strategically) for a candidate they didn’t like because they liked the other candidate even less. This is called “voting for the lesser evil.” It would be hard to create a more divisive situation if that were the goal!
Sometimes, runoff elections are used in an attempt to “patch up” plurality when no candidate has received a majority of the vote. Runoffs do help some, but even runoffs can’t completely make up for plurality’s deficiencies. When there are three or more candidates, plurality is so bad at identifying the correct winner that it is not even guaranteed that the correct winner will be one of the top two vote getters. So the candidate with whom the voters would be most satisfied might not even make it into the runoff election!
There’s more, but that should be plenty sufficient to show how seriously plurality degrades our elections and how urgently it needs to be replaced by a much better voting method.
The Menagerie of Voting Methods
Hundreds of voting methods have been proposed and debated ad infinitum. The states of Maine and Alaska have decided to try a method called instant runoff voting (IRV), which has been used in France. IRV has not proved to be of any obvious great benefit in Maine or Alaska. That’s because although it definitely is much more complicated, IRV is identical to plurality when there are either one or two candidates on the ballot, and it provides only a very small improvement when there are more than two candidates; a large improvement is needed. Some adopters of IRV are experiencing buyer’s remorse. (Note that some sloppily refer to IRV as ranked-choice voting (RCV), which is a category of about fifty or sixty different voting methods—more properly called ordinal methods. IRV is one of the many ranked-choice methods.)
There are also those who advocate approval voting, “score then automatic runoff” (STAR) voting, score voting, and others. Several methods have groups of followers and advocates, but none has been able to convince the others, so the debate has remained unresolved.
Starting at the Beginning
It seems that it would be a good idea to start at the beginning and carefully engineer a really good voting method. That was done in 2020. The very first step in designing something—anything—is to clearly and specifically define what the thing is supposed to do. Write it down. For some unfathomable reason, this key step seems to have been skipped before.
When about to mark a ballot for a particular race, voters all have “opinions” in their brains about each of the candidates in that race. Sometimes, that opinion will be strongly positive for a candidate they consider to be very good—the voter would be very happy and satisfied if that candidate won. Sometimes, the opinion will be strongly negative, and the voter would be very dissatisfied if that candidate won. Of course, a voter’s satisfaction regarding a candidate might be anywhere between strongly positive and strongly negative, including zero (no opinion). It also happens quite often that a voter’s opinion of a candidate is zero because the voter is not informed and simply does not know enough about that candidate to have any opinion—elections with three or more candidates normally have a large number of this type of no opinion.
There are many voters, all with their own sets of opinions about each of the candidates in the race. It is possible (virtually certain with large numbers of voters) that for any particular candidate, some voters will have positive opinions, and some will have negative ones. There will also be some no opinion votes. How should a voting method process this data to identify the correct winner? The only logical conclusion we can reach is that the best candidate is the one who has the highest (or most positive) net total of all opinions (that is, positive opinions minus negative ones). Hence, the definition:
Definition: The best possible choice is that result (chosen candidate) which maximizes voter satisfaction, net of dissatisfaction, when summed over all voters who voted.
There is no better way to translate the collective knowledge, judgment, and wisdom of voters into the best choice. This is the overriding and only objective that a voting method should have.
Much ado has been made over the years regarding the “fairness” of elections and the “fairness” of various voting methods. The term “fair” is subjective and depends completely on what the user of the term thinks is fair. Therefore, the term cannot be used in any rigorous argument without accompanying detailed and objective criteria for what the user of the term considers to be fair. Note that the above definition for the best choice of candidates says absolutely nothing about fairness. However, if one were attempting to define the “fairest” result, it is difficult to think of anything fairer than, in every election, choosing the candidate which maximizes the satisfaction of the voters who voted, just as the definition says.
Carefully Thinking It All Through
It should be clear from the definition and discussion above that a voting method cannot possibly identify the best candidate in all possible elections if it only allows voters to express positive opinions and completely ignores all negative opinions. The missing “magic ingredient” is that voters must be allowed not only to express satisfaction for candidates they like, but also to meaningfully express dissatisfaction or negative opinions for candidates they don’t like.
A voting method has to work well for any number of candidates on the ballot. So, think about the simplest case first: only one candidate is on the ballot (and there are lots of real-world races where only one candidate is on the ballot). Using plurality, this is a sham election! Voters can only vote for the candidate so the candidate will always win. The voters have zero control over the outcome; that’s a sham. That is also true for IRV (and any of the ranked-choice methods), approval, STAR, score, etc. Having more than one candidate on the ballot does not change the voting method, it masks the method’s shortcomings and makes them less obvious!
Knowing that voters must be empowered to vote both for and against candidates is a giant step forward. However, it does not complete the task of engineering a good voting method. There are many ways to design such a method. Which is the best? It turns out that there are some other important things to take into account.
It is known from the Gibbard-Satterthwaite theorem that all voting methods are susceptible to manipulation by insincere or strategic voting, but some are much more vulnerable than others. The Jones Rule also is quite important. It simply says that everything about elections must be understandable by a reasonably bright high school student. If voters can’t comprehend how elections work they cannot participate intelligently and they cannot trust something they don’t understand!
Taking everything into account, the 2020 project concluded that a voting method dubbed Approve/Approve/Disapprove Voting (AADV) is the best choice. Each voter is allowed to approve (vote for) either 0, 1, or 2 of the candidates and also has the option to disapprove (vote against) either 0 or 1 of the candidates. Disapprovals of each candidate are subtracted from that candidate’s approvals to determine each candidate’s net approvals. The candidate having the largest (positive) number of net approvals is the winner. This document explains the complete rules for AADV: AADV Instructions for Voters and Election Officials.
AADV is so much better that it would qualitatively improve elections. Instead of causing polarization, AADV would reduce it. “Extreme” candidates would no longer be nominated as they would garner lots of disapprovals and not fare well. More broadly acceptable candidates with fewer negatives would become the winners. Voters will no longer suffer the agony of having to vote for the lesser evil; instead, they will have the pleasure of voting for the greater good.
Measuring and Comparing Voting Methods
In addition to logically deriving AADV, the 2020 project also made a serious attempt to measure and compare the statistical performance of various representative voting methods by using computers to simulate many hundreds of thousands of elections of all possible types. Many insights were gained through this work. For those interested in all the detail, here is the paper describing that work: Follow-on Election Simulation Leads to Definitive Proposal. For those interested in a complete and thorough treatment of all election problems, see this book: Elections Are Broken — How to Fix Them.
For those mainly interested in the “punchline,” below is a chart comparing some representative voting methods. The chart summarized results from 600,000 elections in which voters voted sincerely. A perfect voting method would have zero errors for any number of candidates on the ballot. (No real-world voting method can be perfect and all voting methods will make some mistakes.) Note the large errors for plurality and IRV. Approval voting does make a noticeable improvement, but AADV is an even larger improvement, especially when there are three or more candidates.
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