If there's "no problem with fractional bits" we are not talking about information. We are also not talking about how to store 10 ballots' results, we're talking about how much information we can retrieve from ONE ballot.
-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Jonathan Lundell Sent: Saturday, June 06, 2009 3:09 PM To: Paul Kislanko Cc: [email protected] Subject: Re: [EM] Some myths about voting methods On Jun 6, 2009, at 11:59 AM, Paul Kislanko wrote: > Besides the obvious problem with the notion of a fraction of a bit, > you're > still confusing the number of possible ballots with the amount of > information conveyed by a single ballot. There's no problem, really, with fractional bits. It's useful to be able to say that a ballot requires (say) 2.5 bits (rather than 3), because it tells us that we can represent 10 ballots in 25 bits (rather than 30). We're just generalizing the number of bits to log2(n). When n is a power of two, we get an integer; else not. > If there are 3 candidates, in approval a ballot only needs 3 bits. > Ranked > ballots need to carry the order the voter selected, and that > requires 2 bits > per alternative. I.e for ballots with ABC, you need 11, 01, 10 to > indicate > B>C>A. You cannot do that with fewer than 6 bits, even though it > only takes > 3 bits to count the 3! = 6 possible ballots. As has already been pointed out, all we need is a lookup table with six entries for the six possible ballots. ---- Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
