[EM] Proportional Representation via Approval Voting

[LAYTON Craig]

Forest wrote (in part):

>Suppose, for example, that forty candidates vie to fill ten seats.  The
>number of ten member subsets of a set of size forty is less than a
>billion.

<snip>

>If the number of seats to be filled is more than a dozen or so, this
>method might not be practical without supercomputer voting machines or

Without some form of shortcut, list system or virtual list on the ballot, I
don't imagine you could feasably have more than six or seven seats to be
filled in any one electorate.  I'm assuming the ideal ballot - a rotated
ballot paper, with candidates listed straight down the paper, not in any
particular groupings or lists.  Odd numbers are best for STV, so seven would
be the optimum number.  For proxy STV it doesn't matter so much, so six
might be better (even seven is a little unwieldy), I'm not sure about
proportional approval.  Depending on how effective constraints on who can
run are, and more importantly how big your electorate is, you could expect
between twenty and seventy candidates for six or seven winners.