Sunday, December 05, 2004
Recounts: A serious proposal
Washington is currently mired in a hand recount of it's governor's race, which came out with a 42 vote margin in the last count. An article here reviews the usual arguments that so close an election can never be definitively counted, due to random errors in either machine or human counting.
That argument is fine under the assumptions, which seem to be a fresh start every time, combined with distractable/fallible/tired humans or machines that lack the imagination to discern unusually marked ballots.
But why start fresh every time? After they are collected, let's number each ballot with some unique identification number. At each recount (i), for each ballot (j), you determine the vote v_ij, such that v_ij = 1 if it's a Rossi vote, and v_ij = 0 if it's a Gregoire vote. As the number of recounts i increases, for each ballot you get a vector of results, v_.j. If v_.j = {0,0,0,0,0}, then we can be pretty sure that's a Gregoire vote; at no stage of the process has a machine or human disagreed. But if v_.j = {0,1,1,0,1}, say, we have identified a problem ballot that needs extra scrutiny.
As the rounds of voting progress, we can segregate the ballots into three bins: those that always count for Rossi, those that always count for Gregoire, and "problem ballots" that get counted different ways. The goal of counting should be to resolve as many ballots in the problem category as possible to everyone's satisfication, and then stop the recounting process when the size of the problem pile is smaller than the margin of victory.
Even with fallible machines and humans, this procedure seems to have a reasonable chance of generating a reliable, accurate count for arbitrarily close elections, provided the counters are fairminded.
That argument is fine under the assumptions, which seem to be a fresh start every time, combined with distractable/fallible/tired humans or machines that lack the imagination to discern unusually marked ballots.
But why start fresh every time? After they are collected, let's number each ballot with some unique identification number. At each recount (i), for each ballot (j), you determine the vote v_ij, such that v_ij = 1 if it's a Rossi vote, and v_ij = 0 if it's a Gregoire vote. As the number of recounts i increases, for each ballot you get a vector of results, v_.j. If v_.j = {0,0,0,0,0}, then we can be pretty sure that's a Gregoire vote; at no stage of the process has a machine or human disagreed. But if v_.j = {0,1,1,0,1}, say, we have identified a problem ballot that needs extra scrutiny.
As the rounds of voting progress, we can segregate the ballots into three bins: those that always count for Rossi, those that always count for Gregoire, and "problem ballots" that get counted different ways. The goal of counting should be to resolve as many ballots in the problem category as possible to everyone's satisfication, and then stop the recounting process when the size of the problem pile is smaller than the margin of victory.
Even with fallible machines and humans, this procedure seems to have a reasonable chance of generating a reliable, accurate count for arbitrarily close elections, provided the counters are fairminded.
