Tags: irv, electoral reform
I like IRV. Let me state that upfront. But I was thinking about its practical widespread adoption and I thought of two issues that I don't see an easy solution for. I'd like to hear answers to issues around recounts and aggregating votes across multiple election offices.
1) Recounts. IRV counting is always done, these days, with a computer. A manual recount of IRV ballots would require more "counts" than a normal ballot. This is because if a particular ballot's first choice is eliminated, the ballot gets recounted for the second choice, and so on. This means, potentially (though not typically) an IRV ballot would have to get counted up to the number of potential candidates. 5 candidates might mean each ballot would have to be counted 5 times in a single IRV count. And imagine the bookkeeping required to do IRV counting by hand.
2) Aggregating votes across election offices. How do votes across county lines (for example) where there are different elections offices counting, supposed to work? How do you "report" a summary of IRV ballots? This is easy to do with straight voting - you simply report the number of votes for each candidate. But with IRV, as the current proposals work, you really can't summarize ballots in this way, because the order of selections on each ballot is significant. I suppose you could figure each possible vote (ie a,b,c a,c,b b,a,c b,c,a), but the number of combinations grows very very quickly for each new candidate added (its a factorial function, for you math geeks). So, for 6 candidates, there would be on the order of 6! (6*5*4*3*2*1) different ways to cast a ballot - about 720 (there actually might be a lot more if you consider the fact that you can leave off a vote for a candidate from the list). Each district could create a summary of ballots in each of those 720 slots. That could be aggregated across multiple elections offices... But if you go to 7, you are looking at 5040 different "buckets". At 8 candidates you get 40320, and I'm being conservative! I guess thats doable with computers. But are people thinking about the aggregation problem?
Are these issues being thought about? Does someone need to write up a "manual to operating large-scale IRV elections"?
Update: I think the number of buckets to characterize a given IRV ballot would be: (where n is the number of candidates) n! + (n-1)! + (n-2)! .. + 1 because leaving off just one candidate lets you have (n-1)! different choises, leaving off exactly two leaves (n-2)! choices, etc. Adding the options of leaving off 1 to n candidates gives you the sum. So, for 6 candidates this is 6!+5!+4!+3!+2!+1 = 720 + 120 + 24 + 6 + 2 + 1 = 873 different ballots for 6 candidates. For 7 candidates, its 5913. For 8 candidates, its 46233. Doesn't affect the total that much.
Update 2: I'm fairly certain my update has the wrong math. Thanks to Harland Harrison, Vice Chair of the San Mateo County Libertarian Party! The correct math for computing the way of selecting and ordered list of m candidates from a field of n candidates is actually n!/m!, no (n-m)! DOH! Pretty basic statistics & probability math. I'll leave the actual numbers as an excercise for the reader.
