[EM] Definition of proportional electoral system

[Kristofer Munsterhjelm]

On 8/28/23 12:13, Luděk Belán wrote:
> Dear all,
> excuse my bad English.
> 
> Can the principle that /if party "A" gets more votes than party "B" then 
> party "A" must not get fewer mandates than party "B"/ be considered a 
> defining characteristic of a proportional electoral system?

It doesn't need to imply propoprtionality. Consider the following method:

The first party (by vote count) gets 90% of the seats (mandates).
The second party gets 5%.
The third party gets 2.5%
The fourth party gets 1.25%
The fifth party also gets 1.25%
The rest get nothing.

This is usually not proportional, but if A gets more votes than B, A can 
never get fewer seats than B, so it passes your principle.

Most proportional methods would pass your principle, though.

Note that some fail a related principle that "if some people change 
their mind and vote for party B instead of A, then A shouldn't gain 
seats at the expense of B". That's called population-pair monotonicity 
or vote-ratio monotonicity. Wikipedia has an article about it here: 
https://en.wikipedia.org/wiki/Vote-ratio_monotonicity

-km