[EM] Droop fails the Markus Schulze Rule

[Markus Schulze]

Dear participants,

some silent participants of the Election Methods Mailing List
asked me to send again that mail in which I have written that
"the aim of proportional representation is to minimize the
number of the wasted votes" and which is interpreted by Donald
Davison to be a pamphlet for the Hare Quota.

I wrote (13 Jun 1997):
> Dear Don,
>
> I have to say something about the Hare Quota and
> the Droop Quota.
>
> Suppose V is the number of valid votes and N is the number
> of the seats of a multi-member contituency.
>
> If the Hare Quota is used, then, if only one seat is
> left, a candidate needs only V/(2*N) votes to win the last
> seat.
>
> This is quite unfair, because
>
> (1) to win the first seat, a candidate needed V/N votes;
>
>     thus the voters won't be equal;
>
> (2) it cannot be expected, that the voters, who are left
>     when only one seat is left, belong to a homogeneous
>     group, because the winner of the last seat will be
>     usually elected by many lower preferences;
>
>     but on the other side, it can be expected, that
>     the voters, who voted for the winner of the first
>     seat, belong to a very homogeneous group, because
>     the winner of the first seat is usually elected
>     by many first preferences;
>
>     thus if the Hare Quota is used, then the voters, who
>     are allocated to the winner of the last seat, would
>     be harmed very much more than the voters, who are
>     allocated to the winner of the first seat;
>
> (3) it can happen that there are more than N groups,
>     which get more than V/(2*N) votes each; and in such
>     a situation, it would be only a question of luck, 
>     which of these groups gets the last seat.
>
> But if the Droop Quota is used, then V/(N+1) votes
> are needed for each seat.
>
> You wrote (at http://www.mich.com/~donald/voter.html):
> > My next reason not to approve of the Droop method is
> > because it lacks the voter representation that can be
> > realized when we use the Hare Quota. The point of
> > proportional representation is to increase voter
> > representation - the method should allow a path for
> > every vote to end up on a candidate that is elected -
> > the ideal would be 100% representation - it is possible
> > to obtain 100% with the Hare Quota. Not so with the
> > Droop Quota which has a mathematical limit that is equal
> > to 100% less one quota. Cambridge elects nine members
> > so one quota is ten percent. This makes the Droop limit
> > on voter representation to be 90% in Cambridge.
> > Ten percent of the ballots are forced to expire because
> > of the math. These ballots may have caused some other
> > outcome of the election. All ballots should be allowed
> > to have a voice in the outcome of an election. Droop
> > Quota is unacceptable because it limits voter
> > representation.
>
> I don't think, that the aim of proportional representation
> is to maximize the voter representation. I think, that
> the aim of proportional representation is to minimize
> the number of the wasted votes. [Example: The principle
> of gerrymandering is to minimize the number of the 
> wasted votes of the own party and to maximize the number
> of the wasted votes of the other party. But gerrymandering
> doesn't change the voter representation. If proportional
> representation is defined using the voter representation
> and not the number of the wasted votes, then it is not 
> possible to explain why gerrymandering is a problem!]
>
> Suppose, there is a single-winner constituency.
> Suppose, candidate A gets 80% of the votes and candidate B
> gets 20% of the votes. Then the number of the wasted votes
> is NOT 20%. The number of the wasted votes is 80%:
> As candidate B is not elected, the 20% for candidate B
> are wasted. And the 60%, which candidate A got more than
> candidate B, are also wasted, because candidate A would
> be elected, even if these 60% didn't go to poll.
>
> Thus the number of the wasted votes in a single-winner
> constituency is always larger than 50%.
>
> And if PR STV is used, the number of the wasted votes
> is always larger than V/(N+1), because:
>
>   Those candidates, who got more than V/(N+1) of the
>   votes are elected even if the Hare Quota is used.
>   Thus all the votes, a candidate gets more than V/(N+1),
>   are wasted.
>
> With regards.
> Markus Schulze