Arrow's impossibility theorem
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Arrow's impossibility theorem
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Re: Arrow's impossibility theorem
#2Can I get a simple wikipedia explanation? That was the most challenging wikipedia article I've ever read.
Re: Arrow's impossibility theorem
#3Can I get a simple wikipedia explanation? That was the most challenging wikipedia article I've ever read.
Try the Stanford Encyclopedia of Philosophy's take on it: http://plato.stanford.edu/entries/arrows-theorem/
It's actually not that "simple", but it's overall less technical.
Re: Arrow's impossibility theorem
#4Can I get a simple wikipedia explanation? That was the most challenging wikipedia article I've ever read.
It is a theorem about the properties of all possible voting systems with preference rankings. The basic idea is there are a few desirable properties for any such voting system, but that it is mathematically impossible for any voting system to satisfy all of them.
Re: Arrow's impossibility theorem
#5Can I get a simple wikipedia explanation? That was the most challenging wikipedia article I've ever read.
It's not Wikipedia, but http://tech.mit.edu/V123/N8/8voting.8n.html may be more intelligible (especially regarding the particular desireable conditions that Arrow's theorem says are mutually incompatible). There's also http://dev.whydomath.org/node/voting/Arrow's_Impossibility_T..., which includes some intuition-building exercises.
Re: Arrow's impossibility theorem
#6Can I get a simple wikipedia explanation? That was the most challenging wikipedia article I've ever read.
In short:
For a voting system (ranking of some candidates based on preferences of voters), it would be nice if:
- A single voter cannot determine the ranking (as a dictator) - For every possible set of voter preferences, there is an outcome (not random) - If everyone likes candidate A over candidate B, then in the final ranking candidate A should be ranked higher than candidate B - If one prefers A over B when comparing just A and B, then one should also prefer A over B when an additional option C is offered
Sounds like some reasonable properties for a voting system, right?
Well, the theorem states that if there are more than 2 candidates, then there is no voting system that has all 4 properties above.
Re: Arrow's impossibility theorem
#7Can I get a simple wikipedia explanation? That was the most challenging wikipedia article I've ever read.
Try the Stanford Encyclopedia of Philosophy's take on it: http://plato.stanford.edu/entries/arrows-theorem/ It's actually not that "simple", but it's overall less technical.
It's technical which is good but much better written than Wikipedia.
Re: Arrow's impossibility theorem
#8Can I get a simple wikipedia explanation? That was the most challenging wikipedia article I've ever read.
It is a theorem about the properties of all possible voting systems with preference rankings. The basic idea is there are a few desirable properties for any such voting system, but that it is mathematically impossible for any voting system to satisfy all of them.
> It is a theorem about the properties of all possible voting systems with preference rankings.
More accurately, it is a theorem about the properties of all possible voting systems where the input is voters preference rankings and the output is also a preference ranking.
Re: Arrow's impossibility theorem
#9Can I get a simple wikipedia explanation? That was the most challenging wikipedia article I've ever read.
In short: For a voting system (ranking of some candidates based on preferences of voters), it would be nice if: - A single voter cannot determine the ranking (as a dictator) - For every possible set of voter preferences, there is an outcome (not random) - If everyone likes candidate A over candidate B, then in the final ranking candidate A should be ranked higher than candidate B - If one prefers A over B when compar…
Are the counterexamples offered by the theorem pathological, in the sense that they are unlikely to occur in practice but are theoretically possible? Or would they arise in practice frequently using standard rank voting systems?
Re: Arrow's impossibility theorem
#10Can I get a simple wikipedia explanation? That was the most challenging wikipedia article I've ever read.
In short: For a voting system (ranking of some candidates based on preferences of voters), it would be nice if: - A single voter cannot determine the ranking (as a dictator) - For every possible set of voter preferences, there is an outcome (not random) - If everyone likes candidate A over candidate B, then in the final ranking candidate A should be ranked higher than candidate B - If one prefers A over B when compar…
Also see http://en.wikipedia.org/wiki/Category:Voting_system_criteria for other potentially desirable criteria for voting systems.
Regarding Arrow's theorem, most voting systems regarded as better than first-past-the-post tend to choose to violate the third criteria, commonly called "independence of irrelevant alternatives": adding another candidate shouldn't change the preference order of existing candidates.