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The point of bringing up Arrow's theorem is to debunk people who claim that certain voting systems are "more democratic" or "better" in some objective sense. What they should be saying is that they prefer a certain voting system because they value certain attributes of voting systems over others.



> The point of bringing up Arrow's theorem is to debunk people who claim that certain voting systems are "more democratic" or "better" in some objective sense.

That's actually an invalid use of it; while the concept of "better" is inherently subjective ("democratic" has multiple definitions, but many of them are objective) Arrow's theorem has nothing to do with that one way or the other.

Arrow's theorem says that a certain set of binary criteria that applies to voting systems that map from a set of ranked preferences to a single preference ranking cannot be met simultaneously, but it does not say anything one way or the other about the ability to differentiate objectively among voting systems on continuous-valued axes, including various operationalisations of "democratic".


Well if that's the point, I definitely disagree with it.

Some voting systems genuinely are more democratic or better than others in an objective sense. For example, a voting system where one person determined by their status in society has their vote count and everyone elses is discarded is objectively less democractic than a voting system where a ballot is selected at random from all voters and is taken to determine the result.

Neither of these systems is as democratic as a system where everyone votes for their favourite and the one with the most votes wins, and that in turn is not as democratic as a condorcet-loser system, where it's not possible for a candidate that the majority rank last to win.

Just because all of the options have problems, it doesn't mean that there aren't options that are completely dominated by others.


> For example, a voting system where one person determined by their status in society has their vote count and everyone elses is discarded is objectively less democractic than a voting system where a ballot is selected at random from all voters and is taken to determine the result.

Obviously this is true, but this is rarely one of the voting systems being considered in any discussion about voting systems.


I'm responding to your claim that Arrows theorem debunks attempts to paint some voting systems as objectively more democratic or better than other voting systems.

If you think that Arrows theorem really does this, then you should stand by that assertion and defend all voting systems that Arrows theorem applies to as not objectively better than any other voting system that Arrows theorem applies to.

And yes, Arrows theorem applies to Dictatorship/Random Ballot/Plurality/Condorcet-loser methods which are the ones I used in my example.


It applies to dictatorship, but doesn't actually tell you anything about it.


I'm not sure the stochastic method you describe, if followed honestly (a big assumption, in practice) would be less democratic than plurality. Your general point stands, though, for sure.


There are reasonable and unreasonable definitions of "fair" and "better". Some voting systems have to have very very unreasonable (to a normal human) definitions of "fair" to be considered superior by any sort of consistent logic.


Arrow's theorem does not say no voting system can be better than any other in an objective sense. It says there is no voting system that is better than every other in every respect.


No, it doesn't say that, either. It says that there is no ranked-ballot voting system that meets a particular set of criteria. (Or, alternatively and perhaps more to the point, it says that the particular set of criteria it sets up are logically mutually contradictory.)


It does say that (about ranked-ballot voting systems), when you consider that each of those criteria does seem a positive attribute of a voting system if nothing else had to be traded away, and which can therefore quite reasonably be viewed as respects in which one voting system can be better than another. It's true that it doesn't apply to scoring systems, but Condorcet's Other Paradox says that no scoring system can be Condorcet consistent so that's a respect in which some ranked ballot voting systems are better in at least one respect than any scoring method.

The general point stands that there is no voting method that dominates every other voting method, but that there can be voting methods that dominate individual other voting methods.




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