Range voting

by on November 12, 2009 at 7:45 am in Political Science | Permalink

A few readers asked me to discuss range voting.  Wikipedia defines it as following:

Range voting (also called ratings summation, average voting, cardinal ratings, score voting, 0–99 voting, or the score system or point system) is a voting system for one-seat elections under which voters score each candidate, the scores are added up, and the candidate with the highest score wins. Range voting was used in all public elections in Ancient Sparta in the form of measuring how loud the crowd shouted for different candidates.[1] Approval voting can be considered to be range voting with only 2 levels (approved (1) and disapproved (0)).

The main question to get out of your head is whether or not range voting satisfies Arrow's Impossibility Theorem.  (In fact it doesn't, most forms of range voting violate the independence of irrelevant alternatives, but don't worry about that!).  There's no major reason why a democratic system should follow all of Arrow's axioms as defined across universal domain, which means you have to rule out the very possibility of paradoxes.  Can anyone do that?  No, not even when you're deciding which book to read next.  (But should you stop reading?  No.)  We do, however, care if the system can:

1. Deliver decent economic growth and an acceptable level of civil liberties.

2. Build consensus and legitimacy going forward, and

3. Toss out the truly bad politicians.

Ideally, we'd even like:

4. The democratic process itself educates people, raises the level of discourse, and makes for a better society.

On those counts, it is not clear what advantage range voting brings over either a two-party winner-take-all system or some form of proportional representation.  Do we really need to count the preference intensity of voters?  That could sooner be harmful in extreme situations.  Do we really need to teach voters complicated aggregation systems?  The relatively well-educated Germans used a "vote twice but ultimately only the party vote counts" form of PR and for decades most of them never understood it and now they are changing it, finally.

Most countries don't use range voting.  Ireland and Tasmania have had some experience with the Single Transferable Vote (STV) system.  What happens is that a bunch of candidates run for each post, party identification is weak, and reps emphasize constituency service.  That's probably the major dominant effect, namely that most systems of range voting weaken political parties.

The bottom line: Range voting is a solution in search of a problem.  The main problems with democracy include poorly informed, irrational, and short-term voters and politicians.  Range voting doesn't cure any of those and arguably by weakening party affiliation it makes some of them worse.

1 DF November 12, 2009 at 8:22 am

I don’t think it violates Independence of Irrelevant Alternatives; rather, I think it doesn’t meet the preconditions of Arrow’s theorem.

To me the issue is (a) how complicated the system is and (b) the likelihood that people will falsify the intensity of their preferences. I can think of candidates I would have liked less than Obama and candidates I would have liked more than McCain, but there would have been no incentive for me to give, say, 25 points to Obama and 75 to McCain; that would be equivalent to throwing away half of my vote.

2 Millian November 12, 2009 at 8:36 am

Have we all been so taken in by the libertarian anti-democracy movement that we forget to add another desirable function about a democratic system:

5. Represents people’s views about economic and social policies?

3 Millian November 12, 2009 at 8:45 am

Apologies for my lack of clarity in posting above. What I’m saying is that a two-party system, with which Tyler seems more than comfortable, can shoehorn voter preferences into bundles which need not represent a coherent agenda at all.

The American eastern working class, choosing between big-business Republicans and bien pensant Democrats, is symptomatic of this problem. In a non-winner take all system, they can establish their own party. In the United States, they have to either vote for things that really aren’t in their interests or effectively disenfranchise themselves by choosing a third party which will not hold a balance of power.

This is undoubtedly a problem that we’d resolve if we could, but looking at the uber-instrumental four criteria presented by Tyler, it doesn’t seem to matter. And why would it, when he sees human irrationality (after Caplan and most of the economics profession) as a problem to be solved rather than as a facet of humanity?

4 TimK November 12, 2009 at 8:56 am

What are the Germans changing?

Tim, Frankfurt

5 jdc November 12, 2009 at 9:17 am

In states like Connecticut where there are already more unaffiliated voters than voters aligned with either party, I doubt approval voting could adversely weaken party affiliation more than the current system. In CT, voters have in effect said that avoiding a strict ideology is more important than the perverting results of primaries left to strongly-affiliated members. As an unaffiliated voter in CT, I’d like to be able to vote for the best candidate without hurting the outcome of the best candidate-I-think-could-win.

6 kai* November 12, 2009 at 9:29 am

“The relatively well-educated Germans used a “vote twice but ultimately only the party vote counts” form of PR and for decades most of them never understood it and now they are changing it, finally.”

In 2008 the German constitutional court ruled the rules for allocating seats unconstitutional because they can produce “negative weight” for votes (i.e. you loose seats by gaining votes).

This sounds pretty horrible, but it has never changed the outcome of an election (i.e. the ruling party). Most Germans prefer this system even as-is to first-past-the-post elections like in Britain and Canada because it is easy to understand how those can produce large majorities for parties that have less than 50% of the vote. (Don’t get me wrong – this is an acquired taste…)

Negative weights are a result of the rather arcane rules of allocating votes. While the German system is very complicated, I think part of this is just inherent in PR – just try explaining the D’Hont method.

Since we are talking about Germany, my guess is that we’ll come up with some pretty arcane fixes to the arcane rules and those surely won’t amount to “changing the system”.

7 Firionel November 12, 2009 at 9:44 am

Just as an aside: I think you somewhat misrepresent the German system as much as the intended changes. (Not that anyone cares around here likely, but still.) The problem any change is trying to address is precisely that in some situations not only the party vote but also the candidate vote change the makeup of parliament as a whole.

8 Jim November 12, 2009 at 10:03 am

No, the main problem with democracy is that in a 2-party system, the political class can easily form a cartel against the taxpayers. Both parties can commit to an ever larger, more expensive and intrusive government — but differ slightly in the implementation details, and yell at each other lot.

The only hope for the taxpayer is be a third-party candidate, but the winner-take-all system makes that nigh impossible. If voters were allowed to rank the candidates 1-2-3, there would be real change. Which is why you will never see it here.

9 dave smith November 12, 2009 at 10:25 am

Wouldn’t cardinal voting collapse into what we have now because voters would lie?

On a scale of 1-100, my preferences last year were Obama 3, McCain 15. I would have voted Obama 0, McCain 100 becuase I liked him better.

That’s just like me voting for McCain in our current system?

10 Peter de Blanc November 12, 2009 at 10:31 am

dave smith: You’re right, range voting usually collapses to approval voting, but that’s not the same as our current system. For example, if there are 3 candidates, you can vote 100 for two of them and 0 for the third.

11 Bernard Yomtov November 12, 2009 at 10:47 am

Voters can actually vote honestly, and don’t have to vote “strategically” by voting for the lesser of two evils.

I’m not sure that’s right.

Suppose you strongly favor X, can tolerate Y, and hate Z. How do you vote? Obviously, Z gets zero, but what’s the X/Y split? 100-0? Any share you give Y risks Z beating X.

But what if X is a serious underdog? Remember, the Spartans didn’t have public opinion surveys (I think). There is is still a strong temptation to vote for Y, the lesser evil, to keep Z from winning.

STV lets you vote for X as #1 and Y as #2 without worrying about this. I live in Cambridge, here we use STV. It’s not without problems, including complexity, but it does let you vote for your preferred candidate without effectively wasting your vote if your candidate is not popular.

12 Ryan November 12, 2009 at 10:56 am

Hmm. I didn’t think I said anything objectionable, but perhaps I’ll rephrase:

In my OPINION, a full array of civil liberties is what is required, not just “a decent leve.”

Furthermore, in the American system the Framers were clear that what they did not want was “to build consensus,” but rather “to establish Rule of Law,” i.e. clear, fair, and just guidelines that people could operate under (and even disagree!). Think about the consensus among voters in the USSR for example…

Sorry if I offended with my earlier comment. Unintended. Too much von Mises leads a person to adopt his method of speaking, which is caustic.

13 Azazello November 12, 2009 at 11:07 am

wouldn’t any rational voter just give maximum value to the candidate he prefers, and zero to any other candidate who might in any way be considered a threat to that candidate? any other split and he’s just working to neutralize his own vote.

14 Matthew Shugart November 12, 2009 at 12:03 pm

No country uses range voting. I would not conflate range voting with STV or cumulative vote.

On Tyler’s paragraph about the supposed effects of STV, political scientists at The Monkey Cage (including yours truly) are weighing in.

15 Scott November 12, 2009 at 12:55 pm

The key statement is “winner-take-all system”. But does it have value in a system that distributes resources based on votes? In that case though it becomes an allocation system.

If you were to tie the budget of an elected person to the net positive range they got there might be value in range voting.

16 Brock November 12, 2009 at 1:23 pm

Suppose you strongly favor X, can tolerate Y, and hate Z. How do you vote? Obviously, Z gets zero, but what’s the X/Y split? 100-0? Any share you give Y risks Z beating X.

But what if X is a serious underdog? Remember, the Spartans didn’t have public opinion surveys (I think). There is is still a strong temptation to vote for Y, the lesser evil, to keep Z from winning.

Give both X and Y a 99 then. There’s no need to “split” any points. That’s still a disadvantage to you though, unless you’re really sure that X is an underdog. Wouldn’t it suck if your points to Y was what cost X the office?

wouldn’t any rational voter just give maximum value to the candidate he prefers, and zero to any other candidate who might in any way be considered a threat to that candidate? any other split and he’s just working to neutralize his own vote.

No, that’s not rational, and you are not working to neutralize your own interests.

Imagine Adam, Bob and Carl are running for office. You love Adam and hate Carl. So give Adam the 99 and Carl the 0. But don’t give Bob a 0! That might elect Carl. Give Bob 50, or 25, or whatever you think he’s worth. Even if Adam isn’t elected, at least you’re doing something to keep Carl out of office.

Range voting is … way too complicated a way to pick elected officials

It’s much simpler than Ranked Choice/Instant Runoff Voting, another popular choice for reformers.

Try this experiment: list 10 movies you’ve seen this year, or 10 books you’ve read. Time how long it takes you to give each a score from 1 to 10 for how fun they were to read. Then time how long it takes you to rank them in order of fun. The latter takes longer pretty much every time.

17 Brock November 12, 2009 at 2:40 pm

you should give 99 to everyone who isn’t Carl

Why? If you prefer Adam to Bob, you would want to give Adam more points than Bob. You still have an interest in seeing that Adam wins. You would have to really, really, really hate Carl for it to be rational to give everyone else a 99.

But even if you did give everyone else a 99, what you’re essentially doing is turning Range Voting into Approval Voting (where every candidate gets a Yes/No from you, instead of a score). And Approval Voting is still better than Plurality Voting.

if you only have 99 points to allocate total …

Ok, but that’s not how Range Voting works.

18 Max Kaehn November 12, 2009 at 4:03 pm

You think a voting system that sticks us with a two-party cartel instead of a diverse market in political representatives isn’t a major problem? Are you sure you’re an economist?

19 Bob Richard November 12, 2009 at 5:57 pm

Arazello’s view of the rational strategy is what I think most voters would do. But it’s not the best answer. The best practice is to give the maximum score to the least bad of the two front runners *and* to all candidates (if any) you prefer to the two front runners, then give zero to all other candidates. This is one of the many problems with score voting: the best strategy is counter-intuitive to most voters. Another problem, as already noted by others, is that it would often degenerate into approval voting. Approval voting would, in turn, often degenerate into plurality, putting is pretty much back where we started.

20 Dale Sheldon November 12, 2009 at 6:08 pm

“Suppose you strongly favor X, can tolerate Y, and hate Z. How do you vote? Obviously, Z gets zero, but what’s the X/Y split? 100-0? Any share you give Y risks Z beating X.

“But what if X is a serious underdog? Remember, the Spartans didn’t have public opinion surveys (I think). There is is still a strong temptation to vote for Y, the lesser evil, to keep Z from winning.”

That’s the POINT. If you can TOLERATE Y, and would prefer them over Z, you can indicate your willingness to compromise on Y by giving them an intermediate score. If half the people feel as you do, and half feel exactly the opposite, than if enough people indicate a willingness to compromise, then the compromise candidate can win.

This is in contrast to plurality (and IRV), where, as per the prisoner’s dilemma, everyone is encouraged to ABANDON the compromise candidate, guaranteeing that about half the electorate (probably more) will be royally pissed off while the other half taunts them for their loss.

Voting shouldn’t be about “winning”: it should be about commpromising on what’s best for everyone. And range voting allows that compromise.

21 Irrational Rube November 12, 2009 at 6:25 pm


Don’t be so sure that Tyler sees human irrationality as a problem to be solved, for on January 21, 2008, he had the magnanimity to gift us with this gem of wisdom:

“But, relative to social democrats, I tend to think that politicians are irrational actors trying to pander to irrational voters and that it can’t be any other way.†

22 Andy McGill November 12, 2009 at 7:30 pm

The parties will just tell their partisans to vote for their candidate and not cast any votes for the other candidates. What is the election agency going to do, throw out those votes? The result is just what we have now.

23 michael webster November 12, 2009 at 10:35 pm

Uh, if the scores are going to be added up, then Arrow’s Theorem is irrelevant as it only applies to ordinal rankings.

I am surprised that Tyler would make this elementary mistake.

24 David Heigham November 13, 2009 at 12:07 pm

Wait a moment. Range voting is accumulating intensitities of opinions, The Ancient Spartan system of deciding by for whom or for what the shout was loudest was range voting. The single transferable vote is not; the rankings it gives are ordinal, not cardinal.

What single transferable votes do in politics is weaken the grip of the party on the rep, appear to make primaries unnecessary, and make it easier for the voters to combine sticking to a party and throwing out scoundrels who happen to belong to the party. Quite a lot of private associations also now use it for their internal elections simply because it sorts out reliably who has the widest (not the loudest)backing among the members.

25 Dale Sheldon November 13, 2009 at 1:15 pm


Well, that’s a bit unfair. Yes, the Spartan’s implemented a range-like system based on making lots of noise; the idea being that more noise means a higher score, and the total noise of the crowd represents the aggregate score of the crowd.

You then make the jump to believe that the winner will be the one with the loudest supporters. That’s not true. You would need a lot of loud supporters, but you would also need just A LOT of supporters. The width MULTIPLIED by the depth of your support would need to exceed that of your opponents.

If it makes you feel better, Venice had a much more “civilized” take on the system.

Although the decorum used in implementing the technique doesn’t really seem to matter: both democracies lasted over 500 years using this system, which is longer than any modern democratic system has lasted.

26 Harald Korneliussen November 16, 2009 at 7:22 am

Dale Sheldon: I wouldn’t know the history of those “bayesian regret” simulations, but I remember some pretty bad assumptions in them, like how to do tactical voting in Condorcet. In range, I can do tactical voting even knowing _nothing_ about my fellow citizen’s preferences, just make sure to use only min and max. And with a simple first-preferences poll the tactical voting will be super-efficient, too, enough that no person would bother voting honestly. In Condorcet, you need far more information in order to vote tactically – if you do it like in range, just blindly burying the top contender, you may just end up hurting yourself – indeed, that’s what your simulations shows. But that is why you don’t DO that in Condorcet. Unless you have privileged information about people’s preferences to the n-th degree, you vote honestly!

As for the extra information in ratings being useless, I’m just repeating Arrow’s argument as I remember it. If you want something sufficently different from me, such as giving extra weight to the opinions of those who are clever at voting tactically, then I suppose it can be useful.

I am a little annoyed myself, at the range-voting enthusiast’s net war. It seems you turn up in every single comment section someone mentions voting systems, and you have a net presence way out of your share of real-world proponents. I remembered reading some interesting things I’d read about using diagrams, with Voronoi diagrams as the proposed ideal. Googling “condorcet voronoi yee” etc. brings up not the original researcher (who supported Condorcet), but the rangevoting.org site’s use of the same! That’s partisan pollution of Google in my eyes. But even at that site, if you read carefully, you can see that RV.org actually concedes that with Ka-Ping Yee’s assumptions, which areused through the page, Condorcet works best – and even that range performs very poorly the moment voters start using even the slightest amount of tactics (normalizing their vote to 0-100). To “save” Range, Smith must propose that 25% of voters vote “tactically” in Condorcet (in fact, use really dumb tactics), and you use “Range with top-2 runoff” rather than proper Range.

That page, IMO, is the most revealing on rangevoting.org. Both its conclusion-before-arguments style, and that it only credits Yee, but does not link to him, or mention that his conclusions are different.

27 DennisP December 12, 2009 at 12:32 pm

Rangevoting.org has been doing computer simulations, and finds that range voting results reflect voter preferences far better than plurality voting. The difference is dramatic: it’s as much an improvement over plurality as plurality is over random selection.

Of course, if the voters themselves are the problem, that’s not necessarily a good thing. Maybe, say, futarchy would be better. But if we’re going to have democracy, and make an attempt to have the will of the voters running things, we might as well do it properly. People who study the mathematics of elections generally consider plurality to be the worst system out there.

Range voting doesn’t exactly strike me as complicated, either. It would be familiar to anyone who’s ever watched gymnastics or figure skating competitions.

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