Sequentially Spent Score: Difference between revisions
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[[Sequentially Shrinking Quota]] is a modification to limit [[Free riding]]
== Related Systems ==
It is the natural extension of the [[Hamilton method]] which is used in [[Partisan Systems]] to [[Multi-Member System]].IN this sense it fits into the Monroe class of [[Proportional Representation]]. Since score is a conserved quantity which is spent like money there is a natural analogy to [https://rangevoting.org/MarketBasedVoting.html Market based voting].
==Criteria==
{| class="wikitable" style="text-align:center"
<!-- criteria headers -->
|- style="font-size:80%;"
! rowspan=1 |
! rowspan=1 style="border-left:2px solid #a0a0a0;" | [[Monotonicity criterion|Monotone]]
! rowspan=1 | [[Pareto criterion|Pareto]]
! rowspan=1 | [[Independence of irrelevant alternatives|IIA]]
! rowspan=1 | [[w:Independence of clones criterion|Clone proof]]
! rowspan=1 | [[Consistency criterion|Consistency]]
! rowspan=1 | [[Participation criterion|Participation]]
! rowspan=1 | [[w:Reversal symmetry|Reversal<br>symmetry]]
! rowspan=1 | [[Favorite betrayal criterion|Favorite<br>betrayal]]
! rowspan=1 | [[Vote unitarity]]
|- style="font-size:80%;"
<!-- Methods -->
|-
! [[Sequentially Spent Score]]
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #fd8787; font-weight: inherit;" | No
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
! style="background: #98ff98; font-weight: inherit;" | Yes
|}
===Participation===
Because this system is a Monroe type which is derived from the [[Hamilton method]] it fails participation. An illustrtive example is as follows.
To simplify lets condsider a 2 seat election in a max=10 score. The candidates are all clones of type A and B.
Case 1:
<poem>30 voters: A=10, B=0
9 voters: A=0, B=10
1 voter: A=1, B=10</poem>
Without the 1 voter giving a score of 1 to A, it would be a tie for the second seat so this score means that A gets both seats. But then if you add one voter.
Case 2:
<poem>30 voters: A=10, B=0
9 voters: A=0, B=10
1 voter: A=1, B=10
1 voter: A=1, C=10</poem>
The extra voter changes the quota size and causes B to get the second seat, even though they prefer A to B.
==== Math Details ====
For Case 1
Score quota = 40*10/2=200
A is the first winner with 301
Ballots spend 200/301 times their support for A
<poem>30 voters: A=3.4, B=0
9 voters: A=0, B=10
1 voter: A=1, B=9.33</poem>
A has 100.66 and B has 99.33. Close but the winner set is {A,A}
For Case 2
Score quota = 41*10/2=205
A is the first winner with 302
Ballots spend 205/302 times their support for A
<poem>
30 voters: A=3.2, B=0
9 voters: A=0, B=10
1 voter: A=1, B=9.32
1 voter: A=1, C=10</poem>
A has 98.36 and B has 99.32. Close but the winner set is {A,B}. So the C supporter ruined it for the second A candidate. This is a failure of participation.
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