The Science

The field of decision science has advanced considerably in the 200+ years since the founding of the country. In the field of voting theory, practitioners have identified many desirable criteria a given voting method may or may not pass. Basically, most criteria define a certain kind of desirable or undesirable outcome, and say that good voting methods should always exhibit or make such outcomes impossible, respectively.

Then Kenneth Arrow, PhD. came along and won the Nobel Prize for proving that it is impossible to construct a "fair" rank order voting system when there are more than two candidates, where fairness was defined by several desirable but now mutually exclusive criteria. This Impossibility Theorem depressed voting scientists for a half a century, for some interpreted as proof that real democracy is provably impossible.

More contemporary work in the field takes a new approach: rather than ask whether a system meets or fails a particular criterion, statistical evaluation methods determine how frequently problems of all kinds happen in a voting system, and how severely those problems manifest in outcomes that are undesirable from the point of view of simulated voters.

Recent work by Harvard Statistics PhD candidate Jameson Quinn models Voter Satisfaction Efficiency - a percentage of how well a voting method performs between selecting the ideal representative candidate versus a random candidate from the field. This study is the first to compare STAR Voting (labeled SRV below) with other systems:

STAR Voting performs at the head of the pack across a wide range of scenarios, and with both honest and strategic voters. In fact, as the chart below shows, STAR's VSE with a 0-5 rating scale outperforms Score Voting with a 0-10 scale, and in its very worst case performs about the same as Instant Runoff Voting's best case VSE scenario:



These results confirm earlier work in the field. Princeton Mathematics PhD Warren Smith has characterized more than 50 different voting systems. Dr. Smith measured voting systems by two key performance measures. First, its propensity to elect the so-called Condorcet Winner. The Condorcet Winner is the one who would beat every other candidate in a head-to-head contest. The second measure, Bayesian Regret is a more comprehensive measure of the overall satisfaction of the simulated electorate at the outcome of the election. Systems that maximize the number of Condorcet Winners and minimize the electorate's simulated regret with both honest and strategic voters are best.

According to Dr. Smith's analysis, rating systems capture the top four spots as measured by both key performance measures of voting system efficacy.


Instant Runoff Voting is at #42 on the list. #41 is the Plurality Top Two. Removing the single choice limit in the first phase vaults a Top Two from #41 to #2.

It's the clue at the top of the list that shows STAR's full breakthrough: a two-phase, one-election hybrid of the Rating and Ranked Choice categories. Dr. Smith's simulations treated that best overall system as a two-election process, Mr. Quinn's according to the one-election rules of STAR. In Mr. Quinn's words, STAR is "unquestionably a top-shelf method."

Science. It works.

The Evidence. A 2012 exit poll study conducted in Manhattan’s 69th Assembly District substantiates the claim that minor party candidates are unfairly marginalized by today’s system. Participants in the study were asked to re-cast their presidential votes using Plurality Voting and a variety of alternate voting methods, including Approval Voting on each candidate. The results were striking:


Although the district is clearly not philosophically representative of the public as a whole, the single choice limitation empirically favors the two best-funded major party candidates. If voters are given the opportunity to rate each candidate equally and independently that all candidates will receive a more accurate measure of voter support.

Showing 11 reactions

  • Samuel McDaniel
    commented 2016-12-04 13:37:39 -0800
    Okay, I understand there is no separate election.
  • Samuel McDaniel
    commented 2016-12-04 13:24:52 -0800
    Why not more than two candidates in the General Election?
  • Paul K
    commented 2016-11-21 16:08:23 -0800
    Ok. I’m familiar with I haven’t seen many of the systems from the above list of 50 described over there, nor anything resembling that list. It’s kind of magic numbers; What does 15,574 Condorcet winner mean? And how are Approval + Top 2; Approval -1, 0, 1; and Approval 0,1 defined? I searched for an explanation and comparison of Score + Top 2 and came up empty before I ever commented here :(
  • Aaron Wolf
    commented 2016-11-21 11:26:21 -0800
    @paul K, all of Dr. Smith’s thorough research and commentary is at the really robust (but not wonderfully designed or edited) site (which is a mirror of )
  • Paul K
    commented 2016-11-21 11:12:42 -0800
    One last question. Where might one find Dr. Warren Smith’s research? I’d like to look at the science rather than a screenshot of the science ;)
  • Aaron Wolf
    commented 2016-11-20 16:52:28 -0800
    @paul K, good question about tie. I’d prefer that the candidate with the higher score wins, but maybe it would just be the same process as a tie in today’s system (whatever that process is).
  • Paul K
    commented 2016-11-20 15:33:00 -0800
    Ok, I understand now. I didn’t realize the percentages on the results graph were from the 2nd round and not merely the approval percentage from the first round.

    Yes, a video would be great!

    Also what happens in the event of a tie in Round 2? Does it revert back to the winner from Round 1?
  • Steven Smith
    commented 2016-11-20 15:23:56 -0800
    Given this confusion, is there any current effort to produce a video illustrating how SRV works (along the lines of the “Six Kittens from Catsburg” video)? Seems like that’d be immensely useful in both clarifying and publicizing the idea…
  • Aaron Wolf
    commented 2016-11-20 14:32:18 -0800
    @paul K, there’s no separate election, the second round just counts all the ballots that scored either of the top two candidates higher than the other one and counts that ballot for that favored of the two.
  • Aaron Wolf
    followed this page 2016-11-20 14:31:22 -0800
  • Paul K
    commented 2016-11-19 06:32:36 -0800
    Neither the page “The Problem and the Solution” nor this page provide an explanation of how Score Runoff compares to simple Score voting. There’s mention of a 2nd stage, but the actual mechanics of the second stage aren’t described. You would do well to have an example election with maybe 10 voters and show how the votes are counted. The score tally is pretty easy to understand, but how is the runoff computed?

    Or is the 2nd stage literally a separate plurality election on some later date?