Proportional representation: Difference between revisions

:<math>\mathrm{SLI} = \sum {(S-V)^2 \over V}</math>

 

The failing of all such measures is the assumption that each vote is cast for one political party. This means that the only system which can be used is a [[Partisan system]]. Under the assumption that [[Plurality Voting]] for a candidate represents a vote for their party, these measures can be applied to plurality voting systems like [[Single Member Plurality]] and [[Mixed-Member Proportional]]. In addition, if it is assumed that when some voters rank every candidate in a party ahead of all other candidates, that they prefer that party, then [[PSC]] and [[:Category:PSC-compliant voting methods | PSC-compliant voting methods]] can be used to measure how well ranked and rated PR methods satisfy partisan proportionality. The consequence of this limitation is that Proportional Representation is not defined for systems without [[vote splitting]].

 

Many of the properties of these systems can be derived from their party list simplifications. The [[Balinski–Young theorem]] implies that not all desirable properties are possible in the same system. Theile type systems reduce to [[Highest averages method|divisor methods]] which means that adding voters or winners will not change results in undesirable ways. The other three reduce to [[Largest remainder methods]] which obey Quota Rules but adding voters or winners may change outcomes in undesirable ways. One such way is failure of [[Participation criterion]]. It is not clear which is a fundamentally better choice since Quota Rules are inanimately tied with some definitions of proportionality.

 

Some common criticisms of [[STV]] (which would likely hold for many other nonpartisan PR methods) are that it is too complex in terms of filling out the ballot and tabulation, that it takes too long to count compared to partisan PR methods (many of which are [[Precinct-summable]] due to being based on [[FPTP]]), and that it can even make representatives parochialist and focused on representing their multi-member districts rather than the state or nation as a whole. Note that this last criticism is inapplicable when nonpartisan PR methods are proposed for a single national/statewide district, though this is usually not proposed or done (with the exception of some 21-seaters in Australia).