[EM] Meek's Method/approval hybrid
Jonathan Lundell
jlundell at pobox.com
Sun May 27 17:12:16 PDT 2007
On May 27, 2007, at 7:55 AM, raphfrk at netscape.net wrote:
> I was thinking about Meek's method and the possibility of combing
> it with approval.
>
> There doesn't seem to be a definition of Meek's method on the
> wikipedia. Does it already allow equal rankings ?
>
I haven't seen an equal-ranking implementation, but Meek had this to
say about it (the papers are available in the early issue or two of
Voting matters):
6. Equal preferences
In section 2 we discussed briefly the effect of different validity
rules on otherwise identical voting systems. The usual STV counting
procedures depend on the existence at each stage of a unique next
preference, the only deviation allowed being, as we have seen, that
the absence of further preferences does not make the vote as a whole
invalid. It is standard practice to accept as valid a vote with a
unique first preference, and to accept further preferences provided
one and only one is marked at each stage; if no, or more than one,
next preference is given at any point, all markings at and past this
point are ignored.
For the simplest form of STV counting, involving the physical
transfer of ballot papers from pile to pile, the need for a unique
next preference is obvious. However, with the feedback method such a
restriction is no longer necessary, and indeed it is not necessary
even with Senate Rules counting. A vote can be marked A1, B1, C2, ...
with A and B as equal first preferences and credited at 0.5 each to A
and B. If A is elected or eliminated the 0.5 is transferred at
reduced or full value to the next preference {\153} which of course
is B and not C. In effect, such a vote is equivalent to two normal
STV votes, of value 0.5 each, marked A,B,C... and B,A,C...
respectively. Similarly, if A, B, C are all marked equal first, this
is equivalent to 6 (= 3!) votes of value 1/6 each, marked A,B,C...;
A,C,B...; B,A,C...; B,C,A...; C,A,B...; and C,B,A... . It is easy to
see that this can be extended to equal preferences at any stage, and
that K equal preferences correspond to K! possible orderings of the
candidates concerned, each sharing 1/K! of the value at that stage.
Such an extension of the validity rules enables us to resolve the
dilemma between the methods (a) and (b) in section 3 of dealing with
non-transferable votes. A voter who, at a certain stage, wishes his
vote, if transferred, to be shared equally between the remaining
candidates, can simply mark those candidates as equal (i.e. last)
preferences. Thus the dilemma does not after all exist; both of the
methods can be used, and the voter himself can determine which is to
be used for his own ballot by the way that he marks it; failure to
rank a candidate indicates a genuine (partial) abstention.
This extension of the validity rules also enables condition (C) of
Paper I to be satisfied more closely. The condition was:
(C) There is no incentive for a voter to vote in any way other than
according to his actual preference.
Here we are interpreting this condition in a particular way not
discussed in Paper I: the STV voting rules not merely encourage but
force a voter to vote other than according to his preference in the
restricted sense that, e.g. if he rates two candidates as equal first
he is not allowed to vote accordingly, but must assign a preference
order between them which may well be arbitrary. In view of the
importance of first preferences in STV, this is undesirable. A voter
is similarly forced to make an unreal ordering of candidates to which
he is indifferent if, for example, he has listed his real preferences
but wishes to give the lowest ranking to a candidate he particularly
dislikes. This kind of voting is very common.
Permitting equal preferences thus gives much greater flexibility to
the voter to express his ordering of the candidates, and is thus a
desirable reform whether the feedback method is used for counting or
the Senate Rules retained.[4]
More information about the Election-Methods
mailing list