[EM] Some myths about voting methods

[Paul Kislanko]

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: election-methods-bounces at lists.electorama.com
[mailto:election-methods-bounces at lists.electorama.com] On Behalf Of Jonathan
Lundell
Sent: Saturday, June 06, 2009 3:09 PM
To: Paul Kislanko
Cc: election-methods at electorama.com
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.
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