Talk:Arrow's impossibility theorem

That was a speculation as to why it hapened. Regardless, it can cause confusion on occasion - and here, where it's rather important to distinguish between individuals and collectivities, it makes a large difference. It would be all too easy to read "they" as referring to the collectivity. (I came across this important distinction in game theoretic stuff like the Tragedy of the Commons, where it actually drives what is going on.)) I think I missed some of the ambiguous usages, so I'll go back and tidy up further. PML.

Where there are only two choices, Arrow's theorem doesn't appear to hold. You can simply apply first past the post, which meets all the criteria mentioned when there are only two choices (meet universality by letting the first voter decide where there is a tie). Do we need to change "among several different options" to "among at least three options"? Martin

Read the theorem again (it's below the list of desired properties), and you'll see that it doesn't claim anything if there are fewer than three options. --Zundark 18:46 2 Jul 2003 (UTC)

Ahh, missed that bit, thanks. But "and the society has at least 2 members" - huh? If the society has only one member, Arrow's theorem holds by non-dictatorship and citizen sovereignty alone, surely? Martin 19:42 2 Jul 2003 (UTC)

You're right that the theorem is true without the at-least-2-members restriction. (But you do need monotonicity to prove this.) The no-dictatorship property can hardly be considered "desirable" in the 1-member case, though, which is probably why the restriction to two or more members was included. You can remove it if you think it's confusing. --Zundark 21:18 2 Jul 2003 (UTC)

Oh yes - of course you need monotonicity - otherwise the method could simply give the reverse of the society member. Neat. :)