Proportionality for Solid Coalitions: Difference between revisions
Proportionality for Solid Coalitions (view source)
Revision as of 07:57, 17 March 2020
, 4 years ago→Types of PSC
No edit summary |
|||
Line 4:
=== Hare-PSC ===
k-PSC
=== Droop-PSC ===
k+1-PSC
=== Hagenbach-Bischoff-PSC ===
[[Hagenbach-Bischoff quota|Hagenbach-Bischoff]]-PSC is the same as Droop-PSC but holds for HB quotas instead, and only requires that the candidates supported by the solid coalition either tie or win when they are each preferred by exactly one HB quota.
The main difference between Hare-PSC and Droop-PSC can be seen with an example: Suppose you can buy two boxes of pizza, with over 2/3rds of voters wanting Cheese pizza, and under 1/3rds of the voters wanting Pepperoni pizza. Hare-PSC would say that you should buy at least one box of Cheese pizza, but has no opinion on what you should buy for the second box, whereas Droop-PSC would say that you should buy two boxes of Cheese pizza. This can be explained as happening partially because if the 2/3rds group of cheese-preferring voters split themselves into two equally sized groups of over 1/3rd of voters each, then these "two" groups that want Cheese would each outnumber the group of under 1/3rds of voters that want Pepperoni.
Line 58:
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 name="The Center for Election Science 2020">{{cite web | title=An example of maximal divergence between SMV and Hare-PSC | website=The Center for Election Science | date=2020-01-31 | url=https://forum.electionscience.org/t/an-example-of-maximal-divergence-between-smv-and-hare-psc/586 | access-date=2020-02-19}}</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 almost always constitute enough Droop quotas (and always constitute enough Hagenbach-Bischoff 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:
{| class="wikitable"
| |||