[EM] Monotonic Proportional Representation System?

Clinton Mead cryptor at zip.com.au
Sun Apr 20 09:38:01 PDT 2003

Is there a monotonic proportional representation system, one that allows 
voters to express their preferences based on individual options, not 
parties or something similar? That is, a system proportional 
representation system that matches these criteria at all times. (Except 
for maybe extreme cases, where there are more options than voters, for 

(1) If option A is selected, then ranking option A higher on one vote 
without changing the order of other preferences must not cause A to 
lose. (Monotonicity).
(2) If there is a set of options X, and N votes who rank options in X 
below only non-selected options and options in X, and N is greater than 
the K * quota, than at least K options in X shall be selected, or all 
options in X. (For example, if 5 votes are A,B,C,D and 6 votes are 
B,A,C,D, and the quota is 8, this criteria dictates that A or B is 

So far I've only found Single Transferable Vote as a individual option 
based proportional representation system, and STV is not monotonic, as 
it eliminates candidates in a similar fashion to IRV, which itself is 
not monotonic.

I was thinking about a possible monotonic proportional representation 
system loosely based on condorcet, but I'm not sure if one even exists 
or if its possible.



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