Difference between revisions of "Proportionality for Solid Coalitions"

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Looking at the top 5 lines, 50 voters, a Hare quota, mutually most prefer the set of candidates (A1-5) over all other candidates, so Hare-PSC requires at least one of (A1-5) must win. (Note that Sequential Monroe voting fails Hare-PSC in this example. However, one could forcibly make SMV do so by declaring that the candidate with the highest Monroe score within the set (A1-5) must win the first seat, for example.) <ref>https://forum.electionscience.org/t/an-example-of-maximal-divergence-between-smv-and-hare-psc/586</ref>
 
Generally, Droop-PSC makes it more likely that a majority will win at least half the seats than only Hare-PSC. The reason for this is that majority solid coalitions always constitute enough Drool quotas to always win at least half the seats, while with Hare quotas they can only guarantee they will win just under half the seats and have over half a Hare quota to win the additional seat required to get at least half the seats. 5-winner example using STV with Hare quotas:
25 A2>A1
 
<br />
{| class="wikitable"
!Number
!Ballots
|-
|26
|A2>A1>A3>B1>B2>B3
|-
|25
|A1>A3>A2>B1>B2>B3
|-
|17
|B1>B2>B3>A1>A3>A2
|-
|16
|B2>B1>B3>A1>A3>A2
|-
|16
|B3>B2>B1>A1>A3>A2
|}
Note that 51 voters, a majority, prefer (A1-3) over all other candidates, and thus electing all 3 of them would mean 3 out of 5 seats, a majority, would belong to the majority. Also, the Droop quota here is 17, and thus by Droop-PSC the majority has 51/17=3 PR guarantees, which would give them a majority of seats. However, by Hare-PSC, they only have 51/20 rounded down = 2 PR guarantees, and thus by Hare-STV:
 
 
 
<br /><blockquote>So, the Hare quota here is 20. A1 and A2 are immediately elected, but post-transfer A3 only has 11 votes, and is thus eliminated first. B1, B2, B3 take the remaining 3 seats.<ref>https://www.reddit.com/r/EndFPTP/comments/ermb1s/comment/ff7a7f8</ref></blockquote>
 
 
 
26 B1>
exists a set C′′ ⊆ W with size at least min{ℓ, |C′|} such that for all c′′ ∈ C′′ ∃i ∈ N′
 
: c′′ i c(i,|C′ |).<ref>https://arxiv.org/abs/1708.07580 p. 8</ref></blockquote><br />
 
== Notes ==