Aggregated Movies Of 2006 List

..that this wasn't jeff-authored...until i thought about the knowledge of mathematics and computer technology involved. still, pretty brilliantly anal. are all of you movie-listers anal? if so, who is the most? i want some rankings, people!

the following dataset:

hardtarget, (7), united, wordplay
hardtarget, (7), united, wordplay
hardtarget, (7), united, wordplay
hardtarget, (7), united, wordplay
hardtarget, (7), united, wordplay
hardtarget, (7), united, wordplay
hardtarget, (7), united, wordplay
hardtarget, (7), united, wordplay
hardtarget, (7), united, wordplay
hardtarget, (7), united, wordplay
hardtarget, (7), united, wordplay
united, (8), hardtarget
united, (8), hardtarget
united, (8), hardtarget
united, (8), hardtarget
united, (8), hardtarget
united, (8), hardtarget
united, (8), hardtarget
united, (8), hardtarget
united, (8), hardtarget
united, (8), hardtarget

the best I can tell (given the alarming lack of transparency) with the aggregate method you'd get:

Hard Target: (10*11) + (1*9) = 119
United 93: (10*9) + (2*11) = 102

Hard Target is seemingly the rightful winner, having garnered a majority of 1st place votes, with a relatively insignificant distinction (albeit positive for United 93) at the end of the lists .

However, if you extrapolate this set 10-fold, with 200 votes cast instead of 20, you get:

United 93: (10*99) + (2*101) = 1192
Hard Target: (10*101) + (1*99) = 1109

Now United 93 wins! Even though Hard Target got a majority of 1st place votes! That was Hard Target's trophy! The effect gets worse the more voters we have, to the point where the first place vote count could be much further apart. It is even conceivable that United 93 could get no first place votes and just walk in to victory by being a middling, uncontroversial candidate compared to Hard Target's edgy avant-gardism.

The aggregate method is undesirable because it is non-majoritarian. However, one could argue that given these are top-ten lists, featuring only movies that have distinguished themselves from the piles of crap also seen by the voter, that what I called a 'relatively insignificant distinction' at the end of the lists is not all that insignificant. This is why the aggregate method is probably less undesirable for this task than for actual election-voting, where people expect a candidate who is the top preference of the majority of voters to win.

but do "people expect a candidate who is the top preference of the majority of voters to win?" yes, this is what they expect. but what's to say this is necessarily the best method?

take the 2000 us election, for example. (ignoring for a moment, the fact that mr. gore won the majority of votes anyway. and the fact that other, much better and more significant and statistically accurate analyses of the election results exist elsewhere. in fact they are everywhere.)

if given the option to rank their candidates, how would things have turned out? for this purpose, i'll throw in nader as candidate #3.

if given the opportunity to rank candidates 1-3, nader voters would have likely voted 1. nader, 2. gore, 3. bush.

bush voters would likely have voted 1. bush, 2. gore, 3. nader.

gore voters whould likely have voted 1. gore, 2. nader, 3. bush.

in all circumstances, mr. gore rates no lower than 2, while mr. bush is the least desirable candidate in two of three situations.

if we assign 3-2-1 values, and give 49% each to mr. bush and mr. gore, with the remaining 2% to mr. nader, our results will be:

gore: 249
bush: 198
nader: 153

ranking the candidates, in this situation gives gore a large victory.

let's try it with buchanan, with preferences being:

gore voters: gore, nader, bush, buchanan
bush voters: bush, buchanan, gore, nader
nader voters: nader, gore, buchanan, bush
buchanan voters: buchanan, bush, gore, nader

and the voting percentages being 49-48-2-1, the results end up:

1. gore: 300
2. bush: 295
3. nader: 204
4. buchanan: 201

buchanan's addition not only narrows gore's victory, but it narrows the factor by which he and nader are virtually out of the race. so while i'm too lazy to search more, perhaps ben is on to something - aggregating, as i have done with our movie lists, pushes the scales towards mediocrity.

imagine if the 2000 election campaign consisted of gore going around the country telling bush voters that he's better than buchanan and bush telling gore voters he's better than nader? come to think of it, it might have been nice, if only for the possibility of a bush-nader debate in front of an army of gore supporters.

very much in favor of a ranked-ballot voting system. all the methodologies deployed by the robot king were variants on instant run-off methodologies that use ranked ballots. i think the straight aggregation of votes however, like nihal says, tends towards mediocrity. that's why you gots to use methods that generate a majoritarian outcome if the votes are there, but also prevents the 'spoiler effect' like we had in 2000.

however this chart makes me think I understand much less about this than I'd like...

IRV voting for all! little american flags for some.