[EM] Arrow's Theorem

[robert bristow-johnson]

On May 4, 2011, at 4:32 PM, Jobst Heitzig wrote:

> Dear Stephen,
>
> you wrote:
>
>> "democratic" implies majority rule
>
> This is by no means clear. You might want to consult this list's
> archives to find some discussion of this.
>
> My opinion is rather that "democracy" and "majority rule" are
> incompatible since the latter assigns all power to 50%+epsilon in the
> worst case, allowing a mere majority to oppress all other voters.
> Democratic group decisions rather require some amount of chance to  
> give
> all voters a fair share of the power.

okay, this is why there is more than one legislator in a legislature.   
we do not want to assign "all power" to any single political  
constituency.  it's also a good reason to have more than one  
legislator seat per district and award office using some kinda  
Proportional Representation method.  perhaps for multi-seat elections,  
Single Transferable Vote is a good way to do it.

but in the case of an executive: a mayor, a governor, a president;  
what would you have us do?  assign the office to the 50%-epsilon  
block?  why might the 50%-epsilon crowd be more deserving to see their  
candidate take office than the 50%+epsilon crowd?

even if the election is close (decided by one vote), i think we all  
agree that, in the case of a binary choice, the choice with the most  
votes (which is the same as a majority) wins.  no?  (if no, can you  
imagine the kind of tactical voting that would result if we award the  
office to the 2nd-highest vote getter?)

both IRV and Condorcet are methods to take the ranked-ballot (which  
translates directly to the traditional ballot, but for *all*  
contingencies) in a multi-candidate race and break it down somehow  
into a simple binary choice.  it's just that Condorcet does it in a  
much more comprehensive and logical manner than does IRV.  all  
Condorcet does is do these hypothetical simple binary elections,  
decided by "simple majority" and apply the results consistently across  
all candidate pairs.

it's sorta like IRV is comparable to the Electoral College (and  
Condorcet to the popular vote).

when the Electoral vote chooses the same candidate for president as  
does the Popular vote, we say that the Electoral College did pretty  
well.  they both agree and some might say the system worked.  (and i  
would say "why bother with the E.C.?")  but when the two voting bodies  
(E.C. and populace) choose different candidates (like in 2000), it  
*never* brings additional legitimacy to the election result.  we never  
say "Phew, I'm sure grateful that we have that Electoral College to  
save us from the imprudent popular vote!"  (some might, if they're on  
the winning side, but they wouldn't be singing the same tune if they  
were on the losing side, so it's a politically convenient position to  
take, not a principled position.)

likewise, when the IRV method chooses the same candidate as Condorcet  
would (which is what would happen if the Condorcet winner makes it  
into the IRV final round), we can say "Hey, IRV did pretty good!"  but  
if IRV fails to elect the Condorcet winner, it doesn't make IRV appear  
more legitimate to the electorate.

so, in both cases; Electoral College and IRV, i would ask "Why  
bother?"  if the measure of goodness of the election result is how  
congruent it is with the Popular vote or Condorcet, respectively, why  
not just use the Popular vote and Condorcet instead of something that  
tries to approximate either?

--

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."