# [EM] General PR question (from Andy Jennings in 2011)

Toby Pereira tdp201b at yahoo.co.uk
Sat Oct 4 15:17:32 PDT 2014

```>> My problem is not that adding the third faction (C) means that the final
>> seat might go to C, but that adding C means that the relative merits of
>> giving the seat to A or B changes.
>I do not understand your concern.  If another faction of voters and
>their candidates join the election and obtain enough votes to merit a
>seat by changing the proportions of votes all other factions and their
>candidates receives, the third set of voters and candidates are
>*relevant* and should obtain a seat.  This is not a case of an
>"irrelevant" candidate or group of voters since the candidate, in the
>case of achieving 1/9th of the votes, this group merits a seat next
>after the other two factions' have, together, elected 3 candidates.
I'm not saying that the C group shouldn't have a seat. What I'm saying is that in your system, adding C changes which out of A or B is more deserving of the final seat, which seems wrong to me. When the first three seats are allocated, with C as part of the election, according to your system, the order of how deserving each group is to the next seat is C>B>A. B is more deserving than A. However, if C is not there, you get A=B. But why should the presence/absence of C make a difference to whether 3 seats to faction A and 1 to faction B or two seats each to A and B is the more proportional result? It shouldn't. In that sense, C is irrelevant. Specifically, C is irrelevant to which out of A and B is furthest from their proportional allocation.

>Given your prior example:>5: A1, A2, A3, A4
>3: B1, B2, B3, B4
>1: C1, C2, C3, C4>How are you redefining the word "irrelevant" to label voting group C
>as "irrelevant"?
It's irrelevant to whether A or B is more deserving of the final seat (regardless of whether C is more deserving than both).

>>So as before, we have:
>
>> 5 voters (A): 2 seats
>> 3 voters (B): 1 seat
>
>> and one seat left to assign. According to your system, it should go to C.
>> However, let's see what happens if we eliminate the B faction and its one
>> seat. We now have:
>
>> 5 voters (A): 2 seats
>
>> and one seat left to assign to either the A or C faction.
>You are, then, entirely changing the number of seats to assign from 4
>to 3?  That should change something don't you think?>If there were four seats, and factions with, respectively 5 and 1
>voter, 3 seats go to the faction with 5 voters, and 1 goes to the
>other.
I didn't use this example initially because I thought you might say this, but no, changing the total number of seats doesn't matter if it doesn't affect the factions in question. All I'm saying is that if faction A already has two seats and faction C has none, which out of these two factions is more deserving of another seat based on the number of voters in each (5 and 1 respectively)? The fact that there might be another faction or indeed several factions with 1, 2 or 79 seats already doesn't change which is more deserving purely out of A and C, or which out of A and C is furthest away from their proportional allocation.

>My method is exactly proportional, not minimizing the "wrong thing",
>and behaves exactly as it should if an "irrelevant" candidate, defined
>in the normal way as a *nonwinning* candidate, drops out of the
>contest.
It doesn't behave as you think it does. My previous examples may not have been clear to you why certain factions were irrelevant, but I will make a clearer case now that works on exactly the same principle.
2 to elect, approval voting
300: A1, A2100: B1
We've agreed before I think that there should be a tie between A1, A2 and A1, B1 (or even A2, B1). The A faction should have 1.5 seats and the B faction should have 0.5 seats. After the first seat goes to the A faction, they both deserve 0.5 seats more, so it result in a tie for the final seat. Now take this example:
2 to elect, approval voting
300: A1, A2100: B11: C1
What should the result be? A should have 1.496 seats, B should have 0.499 seats, and C should have 0.005 seats. A gets the first seat as before. But now, B is more deserving of the second seat than A according to your system. C is surely irrelevant here but it changes the result.
Toby
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