By Mathew Goldstein:

There are currently five declared Democratic Party candidates for each of Maryland's 4th and 8th Congressional Districts and twelve Republican Party candidates for president.  We can expect more candidates to announce soon for these and other competitive primary elections.  The way we in the USA usually select a winner in such multi-candidate, single winner contests is unlikely to select the most popular candidate.  There are alternatives methods for electing candidates that more accurately reflect the electorate's preferences.

We select the candidate with the most votes where every voter votes for one candidate.  We have been selecting election winners this way since before George Washington was elected our first president.  When there are two candidates this method is flawless,and the candidate with the majority of votes wins.  But when there are five candidates, or ten candidates, or more, no one candidate is likely to win a majorityof votes.  The more candidates the fewer votes are needed to win and the less likely it is that the winner will be among the most popular candidates.  

Why do the political parties persist in tallying votes this way in their multi-candidate, single winner primary contests?  There is no one vote per person law for political party primaries.  It is in the self-interest of the political parties to select the candidate most likely to win in the general election.  There is no flawless method to select a winner, but there are methods that can ensure the winner will at least arguably qualify    to be the most popular candidate.  Using computers we can perform the calculations required bythese more sophisticated methods to tally all of the votes in minutes for even the largest elections.

One approach is to let people vote for all of the candidates they like.  This staightforward Approval method works best in contexts where the voters either like or dislike each candidate.  Otherwise voters face a dilemma deciding how many candidates they should approve.  Still, this is better than voters being required to vote for only one candidate.  Now the voters can vote for their favorite, but unlikely to win, candidates and the candidates more likely to win that they prefer to win without sacrificing one for the other.  Voters can vote their ideals and vote their pragmatic compromise at the same time.  The winner will be the most popular candidate as expressed by the voters even when there are many candidates.

Alternatively, we can let the voters express their preferences by ranking the candidates that they favor.  There are different ways to tally preference votes.  Some methods involve tallying a result from first preference votes and if there is initially no winner then second preference votes are added.  For example, if no candidate wins a majority of first preference votes then drop the candidate with the fewest votes and add the second preference votes of the voters whose first preference vote went for the dropped candidate.  Repeat until a candidate wins a majority of votes.  This Instant-runoff method is simple, but this simplicity comes at the expense of not considering all voter preferences to reach the final result.

Can we tally votes to take into account all of the voter preferences in determining a winner?  Yes, we can.  Start by pairing each candidate with every other candidate.  Then we tally all of the voter preferences to determine the winner for each pair contest.  If one candidate beats all of the other candidates then we have identified a most popular candidate.  Otherwise, there are one or more cycles such as a>b, b>c, c>a.  There are several ways to select candidate pairs to be dropped so as to eliminate the cycles until one of the candidates wins all of the remaining candidate pair contests. The candidate who beats each of the other candidates is known as the Condorcet winner.  For those interested in the technical details you can look up the Ranked Pairs and Schultz methods, two well-regarded Condorcet methods.  Some years ago I wrote a Condorcet with Dual Dropping PERL script which is available for downloading free from Sourceforge http://condorcet-dd.sourceforge.net.  

Approval voting has been adopted by the Mathematical Association of America, the Institute for Operations Research and the Management Sciences, and the American Statistical Association.  Instant-runoff voting (IRV) is used to elect members of the Australian House of Representatives and most Australian State Governments, the President of India, members of legislative councils in India, and the President of Ireland.  Variations of Instant-runoff voting are employed by several jurisdictions in the United States, including San Francisco, San Leandro, and Oakland in California; Portland, Maine; Minneapolis and Saint Paul in Minnesota.   The Debian project (a LINUX operating system), the Software in the Public Interest corporation, and the Gentoo Foundation (another LINUX operating system) rely on the Schulze method for internal referenda, leadership, Board of Trustees, and/or Council elections.  The Student Society of the University of British Columbia uses Ranked Pairs for its executive elections.

To enable a meaningful recount when the election results are contested, completed ballots that are simultaneously human and machine readable are printed, verified by the voter, and then machine read. Different machines are utilized to produce the printed ballots and to read the voter verified printed ballots. Voters can don gloves if they want to avoid fingerprinting their completed ballots. As a protection against a  miscount, the number of votes on the individual ballots can be recorded.  For each polling station, the sum of the number of votes from each ballot should reconcile with the contest vote totals (this will work for Approval and Condorcet but not for IRV).

Let’s strengthen our republican democracy by deciding single winner contests with approval or preference voting. Condorcet methods particularly merit favorable consideration in contexts where the contest winner obtains executive authority and where it is common for three or more candidates to compete.