Obscuranym

Be bold!

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NB: I've responded to your question on CRGreathouse's talk page. --Osndok (talk) 19:25, 19 October 2010 (UTC)

From CRGreathouse's page...

Because range voting allows voters to rank candidates equal (or express no opinion at all!), therefore in the theoretical/strictest sense range voting cannot ever guarantee "a unique and complete ranking" (required for arrow's theorem). This is true even with one voter, and is IMHO the quintessential difference between the theory and practice of voting systems (single-voter / ties). Also why 'majority defeat disqualifier' (and other rank-with-equal-option voting systems "fail" arrow's theorem). Cheers. --Osndok (talk) 19:23, 19 October 2010 (UTC)

In my own limited understanding, this isn't really an essential feature of Arrow's Theorem. For example in Freek Wiedijk's "Formalizing Arrow's Theorem" proves the theorem using linear preorders, meaning the theorem continues to hold if ties are allowed. (if the correspondence between the formal proof and the informal description is to be believed, that is). Not to mention that by your description, almost no system technically has the universality principle, as Condorcet's Criterion leads to a 3-way tie when you get a 2/3 winner cycle. (Of course, the probability of that happening with a large number of voters is practically zero...) Obscuranym (talk) 15:56, 20 October 2010 (UTC)

Yes, it kinda is, and... Yes, that's kinda the point. As arrow defined it, absolutely no voting system does. That is why Arrow's impossibility theorem is readily provable, it is very restrictive in it's presuppositions. Approval voting (which can be seen as a special-case of range voting), can be easily converted into ranks-with-equals (e.g. Approving of A & C but not B & D is translated into [A=C]>[B=D]); and approval-voting clearly and demonstrably satisfies the "english" sayings of arrow's theorem (but not the formal b/c of the rank-order limitation). Cheers! --Osndok (talk) 16:56, 20 October 2010 (UTC)

"This" meaning that prohibiting ties between candidates, which is not required for Arrow's Theorem. The reference I gave formalizes and proves Arrow's Theorem while allowing for ties. And that's not the point of Arrow's Theorem: I'm saying that by your description of universality, no voting system is universal! Arrow's Theorem says that certain kinds of voting systems cannot simultaneously satisfy a certain set of conditions. Obscuranym (talk) 17:51, 21 October 2010 (UTC)

I think that you've misunderstood me, but I don't wish to be argumentative. Warren's page on Arrow's theorem explains the range-voting side well (my language can often be computer-esque). To my satisfaction Arrow's theorem proves "you can't have a fair rank-order voting system", yet any fair voting system is provably "equivalent to normalized range voting" (Dhillon & Mertens, Relative Utilitarianism 1999). This is much like turing-equivalence in the computer world, but harder to see. Basically, you can judge a voting system by it's ballot (rank/score, complete/permissive) making only 4 "types" of voting systems AFAICS. --Osndok (talk) 18:53, 21 October 2010 (UTC)

Please be a little bit argumentative, I'm enjoying this conversation, and my understanding of this issue could be better.  :)

I am familiar with Warren's page; at first I didn't believe it, but I found it intriguing enough that I really studied the issue on my own for a while, and eventually decided he was basically correct.

I've heard of the the Dhillon & Mertens paper, but have no opinion on it, as I don't understand it and my deeper foray into social choice theory leaves me dissatisfied with the level of rigor and clarity in the field. From the point of view of not understanding the work, I have two generic objections: first, how correct is the work, and second, why should I accept their assumptions as necessary and sufficient conditions for a "fair" voting system?

And I don't think your description of the universe of possible voting systems is truly "universal", consider for example Declared Strategy Voting or the Iowa Democratic Party's Primary Caucus system, which fall outside your classification system. I have no idea what the phrase "all possible voting systems" really means. =) Obscuranym (talk) 23:45, 21 October 2010 (UTC)

I have not heard of DSV before, so correct me if I'm wrong... but judging from this summary it appears to be (an order of confusion) around strategic voting w/ range-voting ballots. It might be the case that providing "a formula for deciding the input values" is a third ballot alternative, but it still seems like it would have to reduce to cardinals or ranks... where matrices & linear algebra would fall under cardinals. Indeed this statement makes the system sound like an ugly and awful kludge combining range voting and IRV:

"[If] Perot really has a decent chance of winning, voters who give Perot their highest rating will have their votes cast for Perot. But if it turns out that Perot has a slim chance of winning, these voters might have their vote cast for a second choice, depending on how highly they rated the other candidates."

Which if taken at face-value would throw it under rank/preference voting (as "single vote" implies a simple counting). Also concerning the Iowa caucus (which I'm not sure I caught your point at) a higher level formulation of elections (aggregating various election sources/methods) are very interesting wrt multiple winner elections, but they are really more of "recipes" of the ideas of simple elections (usually single-winner). Much like how having a primary election is an interesting way to (attempt-to) circumvent the clone & spoiler effect in pluristic voting, but not really a "voting system" as I would call it. --Osndok (talk) 19:03, 22 October 2010 (UTC)

"all possible voting sytems"

In theory... maybe... :)

"the ballot" - somehow get info from voters

1. score(options) - defined MAX
2. rank(options) - (possibly weighted ranks!)

Somehow reduce to one result

1. aggregate[ballots] - permissive (all info used)
2. aggregate[filter(ballots)] - restrictive (some/all info is transformed or discarded)

So for example

pluristic can be seen as either

pick_max[only_highest(normalize(score(options)))] - restrictive score, or...

max_count_first[rank(options)], - permissive rank

IRV

involved_irv_magic_function[rank(options)] - permissive rank

Range

max_average[score(options)] - permissive score

--Osndok (talk) 19:46, 22 October 2010 (UTC)

Talk:Virtual LAN

I have replied to your comment on Talk:Virtual LAN.. DMahalko (talk) 22:08, 22 October 2010 (UTC)

Sieve of Eratohenes

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