# [EM] Fw: borda count

Steve Eppley seppley at alumni.caltech.edu
Sat Nov 6 11:39:29 PST 2004

```Hi,

> 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
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

```