Juho juho4880 at yahoo.co.uk
Sun Mar 11 12:30:41 PDT 2007

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  
> 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  

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.


> Yours, Jobst
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