The number of possible votes is not the same as the amount of information in a single ballot. With 3 candidates, there are indeed 8 possible ballots, but any one ballot can be encoded in 3 bits, since any particular choice requires only that many to represent it.
Ranked ballots require 2 bits per alternative (01 = 1st, 10 = 2nd, 11 = 3rd) so the minimum ballot representation is six bits, twice as much information as is contained in an approval ballot. -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Dan Bishop Sent: Saturday, June 06, 2009 11:21 AM To: [email protected] Subject: Re: [EM] Some myths about voting methods Warren Smith wrote: > 6=3! possible rank-order votes. However, there are 8=2^3 possible > approval-style votes. Since 8>6, we see the approval voting ballots > provided more, not less, > info, than the preferential ballot. > > Now you may say "but two of those approval ballot types, namely > all-yes and all-no, were silly." In that case there are only 6 kinds > of non-silly approval ballot (6=8-2). > Then still, approval provided SAME info as preferential ballot. Not > correct to say > "it is clear that a preferential ballot has more information than an > approval ballot." > > --let me refute some errors/myths here. In a 3-candidate election, > there are Only works if there are a small number of candidates. Factorial grows faster than exponential. 2^10 = 1,024 10! = 3,628,800 2^20 = 1,048,576 20! = 2,432,902,008,176,640,000 ---- Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
