[EM] Fair and Democratic versus Majority Rules

[Kristofer Munsterhjelm]

robert bristow-johnson wrote:
> 
> On Nov 16, 2010, at 8:57 AM, Kristofer Munsterhjelm wrote:
> 
>> robert bristow-johnson wrote:
>>> On Nov 15, 2010, at 8:40 PM, Bob Richard wrote:
>>>> On 11/15/2010 4:58 PM, fsimmons at pcc.edu wrote:
>>>>> When majority rules, a 51 percent majority can have their way in 
>>>>> election after election. But what other
>>>>> possible standard is there for democracy and fairness besides 
>>>>> "majority rule?"
>>>>
>>>> For seats in legislative bodies, proportional representation.
>>> for which STV or a more Condorcet-like ordering (what would the name 
>>> of that be? Kristofer Munsterhjelm had a Schulze ordering for 
>>> Oakland) does well. here in Vermont we just had an election where for 
>>> my state senate district, we voted for 6 out of about 15 and the top 
>>> 6 vote getters win seats, but that method sorta sucks.
>>
>> Condorcet doesn't give proportional representation. If you have an 
>> example like:
>>
>> 51: D1 > D2 > D3 > D4
>> 49: R1 > R2 > R3 > R4
>>
>> and pick the first four, all the Ds will win.
> 
> good point.  maybe STV would be better for proportionality.
STV would be better since it meets the Droop proportionality criterion 
and Condorcet does not.

>> I think counterarguments would make use of that the majorities are not 
>> necessarily the same. Those who see no point in Condorcet would say: 
>> "if the leftists prefer A to B and the right-wingers prefer A to C, 
>> that's still short of majority rule".
> 
> so let's pick B or C even though a majority of voters (neither 
> specifically left or right) vote that A is the better choice over either 
> B or C.  the reason why Condorcet (assuming a CW exists) is the 
> democratic choice has nothing to do with left or right political 
> alignment.  the problem with electing someone other than the CW is that 
> we, the voters, by a majority have expressed that we want the CW.  
> otherwise, why not use random chance, or just give the election to the 
> *minority* candidate?

I used left and right as examples. The argument would be "so, different 
majority factions wanted someone else, but they're not the same 
majority". I don't agree with it (I would say something like "but assume 
you want X - then you can make a majority more happier by choosing Y 
instead if there's a majority that prefers X>Y").

> here's a fundamental philosophical question: why is it better, even in a 
> two-candidate race, to elect the majority winner?  why not have rules 
> that we elect the minority candidate?  (i have my own answers, but i 
> would be interested in reading some others.)

I would give a practical and a theoretical answer to why one would use 
majority instead of a minority.

The practical answer would apply to all methods contrived to give the 
vote to a minority. Consider a method of the form that "the candidate 
that's ranked last most often wins". Since you're asking the voters for 
their input, the voters would quickly find out that it's in their best 
interest (whenever a majority exists) to rank the preferred candidate 
last. Thus "minority" becomes "majority" - you can't ask the electorate 
to give the answer they'd like the least, because then they'll lie.


Relying on theory, there's the Condorcet jury theorem. If a group wants 
to vote on a yes/no issue, and one (say "yes") is the right answer, then:

if each member has a probability greater than half of getting the answer 
right, then under majority rule, the probability that the group makes 
the correct decision goes to certainty as the group size increases,

if each member has a probability less than half of getting the answer 
right, then under majority rule, the probability that the group makes 
the wrong decision goes to certainty as the group size increases.

Thus, if the voters are smart enough and the group is large enough, 
you'll get the right answer by majority rule and the wrong answer 
without it. If the voters aren't smart enough, then the optimum is an 
enlightened dictator. If you can appoint enlightened dictators in a 
robust manner, then you don't need voting, and if you can't, the same 
logic holds for the question of whether the voters are smart enough to 
pick the dictator by majority vote.