[EM] Meek's Method/approval hybrid

[Jonathan Lundell]

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]