[EM] Fw: borda count

[Steve Eppley]

Hi,

Mike (R?) asked:
> Here's a similar question: Does it matter if we use 
> a Borda count of 3-2-1-0 (Highest score wins) or 0-1-2-3
> (lowest score wins)? I thought I read somewhere they
> weren't necessarily symmetric, but I can't think of 
> any counterexamples so I might be mistaken. 

Again, as Stephane pointed out for 4-3-2-1 vs 3-2-1-0,
it depends on how non-strict orderings are handled.
Assuming all votes are strict orderings, "3-2-1-0 
highest wins" elects the same winner as "0-1-2-3 
lowest wins."

> I *do* think the lowest score wins version makes it
> easier to compare elections with varying numbers of
> candidates if you are going to use the Borda count
> anyway.

If the point is to compare results having different 
numbers of candidates, you might instead wish to normalize 
the results by dividing by the number of candidates
or dividing by the sum of scores.  One of these 
approaches may agree more closely with people's 
typical expectation that bigger is better.

I'm not sure why I'm spending time discussing Borda
variations, though.  They all suffer from an egregious
violation of clone independence that would lead to
a race to nominate as many clones as possible.  

Don Saari claimed in a recent opinion piece in the 
Los Angeles Times that he recently proved Borda is the 
best voting method.  But he didn't list his assumptions.
Did he assume the set of candidates is fixed, not 
strategically nominated?  Did he assume all votes are 
sincere?  Did he assume some unimportant criteria 
such as reinforcement & participation are important?
Several years ago he gave a talk at Caltech (to hype 
his book "The Geometry of Voting") and afterward
I asked him about Borda's problem with strategic 
voting. (I don't recall asking him about strategic
nomination; I think his talk occurred before I'd
heard about clone independence.)  He replied he was 
not a political scientist and did not take into account 
any such considerations.  Unfortunately, that doesn't 
seem to deter him from advocating the use of Borda 
in political elections.  :-(

I like the anecdote Salvador Barbera mentioned in his 
course on strategy-proofness when he visited Caltech 
one year.  He cited a prestigious (but unspecified)
department of economics at some European university,
who wanted to add another person to the department.  
There were 4 candidates: two were world-class economists, 
one macro and the other micro, and the other two were 
merely mediocre, with one clearly better than the other.  
Everyone sincerely preferred the two world-class 
economists over the two mediocre economists.  The 
members of the department used Borda to vote on it.  
Each member understood Borda strategy: those who wanted 
to hire the macroeconomist ranked the microeconomist 
last, and those who wanted to hire the microeconomist 
ranked the macroeconomist last.  Since the better of 
the two mediocre candidates was ranked 2nd by everyone, 
he won the election.  They violated weak Pareto!

--Steve