Guest Post: An Introduction to Score Voting: The Only Way Out

by Dale Sheldon of Least of All Evils

Why is score voting something you should know about? The root cause of the two-party system is not a grand political conspiracy, nor a willfully ignorant populace. Rather, it is a direct result of rational responses to the incentives provided by our voting system. Therefore, the only way to escape the duopoly is to change those incentives. Score voting is the only voting system that can do that.

Before I describe the mechanics of score voting, let's look at the incentives that bind us to the two-party system. There are several ways to slice the issue, but it can be boiled down to two facets. Number one is the incentive toward lesser of two evils voting, or favorite-betrayal, where, even though we may want some third candidate to win an election, there are situations in which voting honestly will cause the worst candidate (from our perspective) to win; and so, the voter benefits from betraying their favorite. The second is the incentive against cloning. When two candidates with similar platforms run, they tend to split the vote between them and allow a third candidate to win, even if a majority of voters would prefer either of the first two. The incentive here is for political parties to put forward only one candidate for office (this is why we have primaries) who is as non-offensive as possible, and also to attempt to discredit or destroy third-parties who are close to them in outlook.

Many attempts have been made over the years to devise a more-perfect voting system, with the goal of minimizing the effects of these bad incentives: the
Borda count, Condorcet's method, instant-runoff voting, and many more. Our present system, plurality is hands down the worst offender, and each of these alternatives is an improvement, but it has been mathematically proven that none of them can eliminate both incentives entirely. But score voting can.

Score voting works like this: every voter gives every candidate (or any sub-set of candidates) a score, taken from some predetermined range of values. This is why score voting is sometimes also called range voting. Typically suggested ranges are 0-9, or 0-99, or 0-1, which gives you the most minimalistic form of score voting, called approval voting. There are no restrictions on the scores you can chose; they don't need to sum to some number, and you're not barred from giving the same number to multiple candidates. The winner of the election is the candidate with the highest average score. That's it!

You might be surprised to hear that such a simple system is the only one that can eliminate the perverse incentives of our voting system –and I'm sure there will be some people in the comments who will claim I'm incorrect–, so here's the evidence:
this paper (pdf) by Dr. Warren Smith, professor of mathematics at Temple University, elegantly proves that score voting surpasses all other commonly-suggested alternative voting systems. It can do this because all other systems rely on ranked-order ballots, where you list the candidates in the order you prefer them, rather than scoring them each independently as score voting does. This finding was the result of eight years of investigation by Dr. Smith and his associates, following the surprising results from Smith's earlier work, which consisted of a massive election simulation experiment that pitted dozens of election methods against each other in millions of votes among thousands of voters, to determine which one, on average, produced the best outcome for the electorate. Score voting had been included on a whim; no one had seriously expected it to perform well, but the results were astounding (see this graph with explanation) and compelled Smith to found the Center for Range Voting to investigate further, and determine why it was so effective. Today, armed with these results, CRV is beginning the work necessary to implement our theories, and we need your help! If you want to rescue our democracy from the dungeon of our two party system, there really is only one way out, and it's score voting. Please, stop by The Center for Range Voting to sign up or examine our information, or ask your questions in the comments and I will do my best to answer them.


d.eris said...

Has range voting already been implemented anywhere in the country? If not, where or in what context is it already being used? Thanks for the post, Dale.

Dale Sheldon-Hess said...

Score voting is not currently being used for elections to any political offices in the United States.


* There are many professional organizations that use approval voting (i.e., range with a 0-1 range).

* Score voting is used in many non-electoral capacities which require a decision among more than two candidates, such as in some Olympic events (imagine the judges deciding the gold medalist by plurality voting!), or the Internet Movie Database's "Top 100 Movies of all Time" project (hundreds of thousands of "candidates").

* Score voting was used historically in the Republic of Venice (with a range of -1 to 1), as well as the Greek city-state of Sparta (sort of; rather than submit a number, voters simply yelled at a volume to match their enthusiasm for each candidate); perhaps not coincidentally, Venice and Sparta are the two longest-running democracies on record, each having survived for about 500 years.

Anonymous said...

Interesting post, never heard of this before. But some places are moving toward IRV, doesn't that already solve the duopoly problem? Why go with something no one's ever used before?

Dale Sheldon-Hess said...

No, IRV does NOT solve the duopoly problem. IRV is a rank order ballot system and so, by Dr. Smith's proofs, we know it must fail either the favorite-betrayal criteria (FBC) or the independence-of-clones criteria (ICC).

Now, we know that IRV passes ICC, but it FAILS FBC; in other words, under IRV, there are times when it is in the voter's best interest to vote for the lesser of two evils. Most IRV advocates INCORRECTLY state that IRV never encourages you to betray your favorite, but this is simply not true; (and my blog at has multiple easy-to-follow examples and data to show this.

The damaging effect of this failure is supported in experiment and in practice: in experiments, IRV leads to _precisely_ the same results as plurality with strategic voters (and even with 100% honest, non-betraying, (and self-defeating) voters, IRV is on-par with 100% strategic score voting; and most voters (50-90%)choose strategy over honesty.))

In practice, Australia has used IRV for many many years, and across all of its IRV-elected seats (the lower congressional house), it is two-party dominated, to the same degree which the US is under plurality. (Meanwhile the upper house uses a form of proportional representation, and consist of about 9% third party candidates.)

I repeat: IRV DOES NOT FIX THE PROBLEM. I cannot stress that enough. Implementing IRV would be a whole lot of work for almost zero practical gain; better to make a change that will be effective, rather than squander the political will to implement change on something useless like IRV.

d.eris said...

One big difference between our current method and score voting, it seems, is that today we vote for just one candidate in a given race, while with score voting you would rate every single candidate in that race. If a voter only rated the candidates they like, would the other candidates receive a zero? There might also be some resistance among the populace here insofar as it might be perceived that score voting infringes upon the "one man one vote" principle, though I wouldn't argue that it does.

I'm also thinking about tallying methods. (I don't know much about the mechanics of vote counting in general.) Is this something that could only be done by computer? Or would hand-recounts be possible too? Or is it really not any different from the current plurality system in so far as the mechanics are concerned?

Samuel Wilson said...

I'm curious about the historical thinking behind the case for score voting. Is it the view of score-voting advocates that plurality elections make a two-party system inevitable? A lot seems to depend on whether plurality voting always devolves into choosing the lesser evil. Not to be too literal about it, but doesn't a lesser-evil impulse imply a perception that some party is "evil?" Is it automatic that plurality elections will encourage that perception? Or could we yet have plurality elections in which no candidate is considered by any voter to be the "worst case scenario" that must be thwarted at all costs, and each candidate is appraised objectively on his or her merits? I don't raise these questions as an attack on score voting, but for clarification of the supposed historical necessity of it.

Dale Sheldon-Hess said...

"If a voter only rated the candidates they like, would the other candidates receive a zero?"

Good question.

It depends, because you can answer the question in many ways and still have a system you can call "score voting."

You can give un-scored candidates a zero; and the concern there is that good, but un-known candidates will do very, very poorly; to which detractors say "if they can't get their message out, I don't want them to win anyway."

Alternately, you make the "default" score be "do not include the voter in the average": so if 1000 people vote in an election, but 200 of them leave the score for candidate B blank, then you take the average ONLY of the other 800. In effect, by not scoring a candidate, you're saying "I trust the rest of the electorate to decide" on them. And the worry THERE is "what if some mad-man gets on the ballot and no one notices except his handful of mad followers and they all give him the top score and he wins!" Which seems a bit of an odd worry (since getting on a ballot is hard and draws a lot of attention, particularly if you're mad), but let's assume there is some small chance of that being a problem.

The current recommendation from CRV is somewhere in between. It suggest "padding some zeroes" into each candidate's score. Let me give an example: say that we set the number of zeroes to pad, the "quorum", at 100 votes. In the election, there are 1000 voters, and 800 score you (so, 200 do not); your total score is the sum of the 800 votes you received, divided by 900: 800 votes, plus 100 quorum. So if a madmen got only ten votes, even if they were all at top-value (say, 9 on a 0-9 scale), his total score would be (9*10)/(10+100) which is less than 0.82; he'd lose terribly.

As for what to set the quorum at, I don't think CRV has a recommendation, but something like 1.5% of the number of votes in the most recent presidential or gubernatorial election is probably a good guideline. Incidentally, in most states you need about twice that amount (3%) of signatures to even get on the ballot.

In practice, when voters don't know anything about a candidate, they tend to vote them very, very low, rather than leave them blank, anyway. But a quorum rule of some kind is possibly a good way to alleviate some of the (perhaps unreasonable) fears some people would have about the system.


As for one man, one vote complaints: poppycock. The Minnesota supreme court just recently found that ranked-order ballots were NOT a breach of "one man one vote", and the same logic applies to scoring-based ballots. Thomas Jefferson himself was well-familiar with, for instance, Condorcet's method (which uses ranked-order ballots) and certainly intentionally left the door open for the possibility.

A "vote" is not, by necessity, a single name, so what's important isn't "one man, one name on a ballot"; what's important is "one man, one ballot"; it doesn't matter what that ballot is, as long as everyone's ballot is treated deterministically and equally.

Dale Sheldon-Hess said...

"Is it the view of score-voting advocates that plurality elections make a two-party system inevitable?"

Yes. This suspicion is best known today as "Duverger's Law", and has been born out by pretty much every modern democracy everywhere, and is backed by theorem, simulations, and real-world examples (all available by poking around at

"Evil" is, of course, a euphemism. But logically, there must a candidate who is "least preferred", whose victory would be considered at least "less good", and that's all it takes to drive the two-party lock.

I should point out a number of caveats though:

One that Duverger's law is about plurality use in *single-winner* elections; proportional representation, then, can help alleviate the problem (and it does, somewhat).

Two, all politics is local politics. In India for example, there are many more than two parties, but almost all of them are local to a single state or even smaller administrative district. Each locale, though, usually has only--take a guess how many--two parties that are considered "viable" in that locale.

Three, parliamentary systems, like England (or, again, India) are less-affected by this, for a number of reasons, while nations like the US and Australia who directly elect the head of state, are more-prone to the problem (that said, it's not a perfect fix, and I prefer the way we do it here in America anyway, and so seek to fix the problem in other ways.)

Four: it's a tendency, not an iron-clad inevitability (third parties aren't COMPLETELY gone, just very very small), nor is it permanent. There have been times where the top-two parties have changed (remember the Whigs!)... but these moments of transition are infrequent and often strife-ridden eras (I recently did a five-part series on precisely that topic over at

Finally: the piece was written to Poli-Tea's readers, which I presumed are already anti-duopoly; but if that's not the case, I have many more arguments in favor of score voting to provide (such as measures of Bayesian regret) which you can find at the CRV webstie ( or or at my blog (

Dale Sheldon-Hess said...

I just noticed I missed the third question buried in d.eris's last comment.

Score voting is easy to do by hand, but not quite as easy as plurality; you can't just separate the ballots into piles, since each ballot effects the score of multiple candidates. Instead, it's easier to pick one candidate, separate the votes into piles by the score for that candidate, count each pile, and then repeat
that for each candidate.

Pretty easy, but of course not as easy as plurality.

But score, like plurality and UN-like IRV, can easily be run on every mechanical or electronic voting machine in America today (for older machines the workaround involves replacing each election with one candidate from the election, and the candidates for each election with the scores for that one candidate; from there the total score is easy to determine with a bit of arithmetic, although you do end up using many more "lines"; there are work-arounds for IRV but they are, shall we say, quite a bit more error-prone), and has meaningful precinct-level subtotals.

d.eris said...

Though it has a parliamentary system, India is a good example of how even though Duverger's law still holds, you still end up with a multiparty system. I've made this point before elsewhere, but I'll make it again I suppose. Imagine, for instance, if the Republican Party simply died out in the northeast, it is already pretty close to extinct in a number of quarters there anyway; and that the Democratic Party withered away in a number of strong Republican states, Duverger's law would suggest that in each of these locales another party or force would arise to fill the gap. Thus, you could end up with a situation where even though at the local or state levels you still had a two-party system, nationally there would effectively have multi-party government.