Juho wrote:
Few notes.
In some cases having an opposition may be a positive thing. E.g. having
always the same government may not be a good thing in the long run.
One approach is to use some single winner method to determine the
preferred coalition that should form the government (I'm assuming a
multi-party system here) (candidates in the single winner election are
coalitions like "Party1+Party2", "Party1+Party3+Party4" etc.). That
could lead to either a majority or a minority government, consisting of
one, few or all parties.
That could be an interesting way to solve the "indecisive parliament" or
"frequent government change" problem where these exist. In order to
recall the executive, they have to vote for a new coalition at the same
time. If the winner passes a certain threshold, the old
government/executive is removed and winning coalition gets to decide the
composition of the new government; otherwise, nothing happens.
That would be workable for matrix voting in general, too. Use the matrix
vote to find the n best governments. In a proportional matrix voting
system, the alternatives would be chosen in a way so that the
alternatives' supporters overlap as little as possible. Then those n
options are brought to a single-winner vote, and if the winning set
passes a certain threshold, the government/executive is replaced;
otherwise, nothing happens.
The greatest problem here, I think, would be if the opposition agreed to
pick some random (or otherwise undesirable) government and coordinate
their votes, and the treshold is short of a majority. Then the new
opposition does the same, and the government cycles back and forth.
Also, the threshold constraint makes single-winner criteria applicable
to the second round. Governments that are alike except for one single
member would "split the vote" in a bad single-winner system, just as
candidates do in general elections.
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