[EM] Simplified ranking in real elections

[Bart Ingles]

Dear Hugo:

>From my own point of view, any advantages to even the best pairwise
ranked methods over approval voting are more theoretical than practical.

First, the two types of methods are likely to agree more than they
disagree.

Second, when the methods do disagree, there will be cases where either
method produces the (arguably) better winner.  Most of the time these
different winners will be of comparable popularity (depending on how you
measure "popularity").  But occasionally the differences will be
substantial, as in the case where Condorcet or Borda methods choose a
candidate with essentially zero utility.

For example, suppose the voters rate candidates on a scale of 0-10:

  % Of
  Votes     Candidate(0-10 rating)
  -----     ----------------------
   49%        A(10)  B(1)  C(0)
    3%        B(10)  A(9)  C(0)
   48%        C(10)  B(1)  A(0)

Here candidate B is the Condorcet or Borda winner, even though 52% view
candidate A as highly qualified (a rating of 9 or 10), and 97% despise B
(with a rating of 0 or 1).  Using approval voting, candidate A would
almost certainly have won.

I have never been able to find an example of the reverse -- at least not
one nearly so extreme.  It may be that when the two classes of methods
disagree, the tradeoff is that pairwise methods are slightly better more
frequently, while approval voting is better at avoiding the less
frequent very bad result.

In computer simulations across many election runs, the two classes of
methods seem very close in terms of overall utility, with a slight edge
going to some of the pairwise methods.  But to me, avoiding the
occasional disaster is more important than a slight difference in
average expectation.

It's possible that with some of the ranked methods, strategic voting
might help to avoid the above outcome, but there doesn't seem to be much
of a consensus on this point.  Also, such a result is probably less
likely (but not impossible) when there are many candidates.

If you must use ranked ballots, then I agree that some sort of
restriction in the number of ranks is worth considering, but I would try
to make it a function of the number of candidates in the race if
possible.  So for up to four or five candidates, you could allow two
possible rank positions (essentially the same as approval voting), and
then gradually increase the number to some practical maximum (maybe
three or four rank positions) when there are many candidates.

This would help avoid outcomes like the one above in small candidate
fields (where they are most likely to occur), but still allow the voters
to fine-tune their preferences with larger candidate fields.

I don't know how important this fine-tuning really is, though.  To me,
if you have 20 candidates, and a subset of two or three are much more
popular than the others, it's more important to guarantee that a member
of this subset is elected, than to worry about exactly which member. 
This seems analogous to the Condorcet cycle situation, where Condorcet
supporters often argue that choosing from the Smith set is more
important than worrying about which Smith set member is chosen.

Bart Ingles



Hugo Harth wrote:
> 
> Direct election of local mayors in Flanders (Northern Belgium)
> 
> Formerly the mayors were elected by the local councils.
> The direct election of the mayors by the population is now being prepared
> (due 2006).
> 
> If we think about ballots were the candidates are ranked (SSD, Tideman,
> ...), then we may expect some practical problems.
> The theoretical procedure may be too cumbersome, especially for the voter.
> 
> The larger cities may have 20 or more candidates, possibly some belonging to
> the same party
> (so far I am not aware of an interdiction of multiple candidates of the same
> party running for the mayor-seat).
> Voters will not or only grudgingly rank 20 candidates.
> 
> I believe this a simple and reasonable simplification, but I would like to
> hear comments or perhaps hear about simulations or other tests.
> 
> The simplification thought of is :
> On the ballot there will only a restricted number of ranks possible (perhaps
> 3 ... 5)
> and in most cases less than the number of candidates.
> People may rank a candidate only once (of course) or not.
> Not ranked candidates receive the lowest rank (one lower than the lowest
> rank on the ballot).
> People may rank several candidates in the same rank (example, think of
> people liking a particular party more than another who would rank in the
> same way all the candidates of a party).
> 
> The Dodgson or vote-matrix is now incremented as follows :
> For every pair of candidates, compare their ranks, if they are different,
> the cell of the winner-pair in the vote matrix is increased by 2.
> If the ranks are the same for candidates i and j, both cells (i,j) and (j,i)
> are increased by 1.
> 
> Most voting is now by computer (last elections were held in 2000).
> Voters use a light-pen and press on bullets on the screen.
> Part is still be done by paper-ballots.
> These are analyzed either manually or mechanically.
> 100% computer-voting may be thinkable in 2006.
> 
> Your comments on this or other simplifications are welcome.
> 
> yours sincerely,
> 
> Hugo Harth
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