On Mar 10, 2007, at 21:31 , Jobst Heitzig wrote:
Dear Forest,
you wrote:
At the other extreme, suppose the election is presidential, and one
voter bullets for write-in X, and no other voter even approves X, and
that the first ballot drawn is the bullet for X. Then under D2MAC
candidate X wins.
The reason I suggested D2MAC was foremost to show that democratic
methods are possible in theory.
I think term "democratic" is not a good term to describe the fact
that methods like D2MAC and random ballot give all candidates some
positive probability of winning. I think e.g. term "proportional"
would be more accurate (since the "fairness" of these methods will be
demonstrated after multiple candidates have been elected
sequentially, in the same way as multiple winners can be elected
proportionally in multi-winner elections). Not being "proportional"
doesn't necessarily mean that the method would be less
"democratic" (see e.g. my further comments below).
In practice, one will have to make sure only such options that are
in a
certain sense "feasible" are on the ballot. Write-ins would not
automatically pass as "feasible" unless the electorate is small and
voters trust each other not to suggest "unconstitutional" options.
Feasibility of all options on the ballot could be checked by an
independent institution, say a high court or mediator.
A different approach would be to combine a democratic method like
D2MAC
with some kind of "supermajority veto": all suggested options must be
registered before the decision, will appear on the ballot, and each
voter can mark an option as "unconstitutional"; options which are thus
marked by more than, say, 90% of the voters are considered infeasible
and are removed. This, of course, requires responsible voters who
really mark unconstitutional options.
If one adds new such criteria to the method that have an influence on
who will be elected, that combination of methods could be called a
new voting method (that may take place in two phases as in your
examples above). It is also possible to see the target social utility
function to be different then, not giving all candidates the
possibility to win but always favouring the "centrist" candidates (or
"constitutional", "non-vetoed", "feasible", or simply the "more liked
ones").
Note also that in some elections it may make sense to allow only very
few strongest candidates to win (i.e. not only the worst ones would
be denied the right to victory but also some relatively popular
ones). As an example consider presidential elections in a country
where president has lots of power (police, military). 1/3 of the
population supports a candidate that wants to do something really bad
with the power he would have. In this kind of countries the rules of
presidential elections could well be such that the 2/3 majority that
strongly dislikes the plans of "the 1/3 candidate" could make it
impossible for that candidate to be elected. This can be said to be
one of the benefits of the majority rule. My point here is just to
demonstrate that elections methods that automatically limit the
winning probability of some marginal candidates to 0 can be useful
and natural in many elections. This does not mean that all elections
would be like this. Random ballot and D2MAC (and their different
utility targets) may well be good methods for some other elections.
Juho
Yours, Jobst
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