On 8/28/23 12:13, Luděk Belán wrote:

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

Thank you for answer.
I didn't express myself accurately. I wanted to know whether the mentioned
principle is a necessary condition of a proportional electoral system, not a
sufficient condition.

Luděk Belán

---------- Původní e-mail ----------
Od: Kristofer Munsterhjelm km_elmet@t-online.de
Komu: Luděk Belán LudekBelan@seznam.cz, election-methods@electorama.com
Datum: 28. 8. 2023 13:23:10
Předmět: Re: [EM] Definition of proportional electoral system
"On 8/28/23 12:13, Luděk Belán wrote:

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
"

On 2023-08-28 13:46, Luděk Belán wrote:

It might be, for quota-based proportional representation.

The Droop proportionality criterion says that if a solid coalition (in
this case, a party) obtains more than 1/(n+1) of the vote, it should get
at least 1/n of the seats.

So if we have two parties for two seats, and one party has more than 33%
of the vote, then it must get at least one seat. Then the other party
also has more than 33% and must get the other seat. So there's no room
for nonmonotonicity in the mono-add-plump sense (i.e. additional votes
for A won't harm A).

For things that generalize Webster and other divisor methods, it's even
easier: the party list case is just Webster (or D'Hondt or etc.), which
themselves are monotone functions and so pass your condition.

Things get a lot messier for ranked voting methods, though, because
"votes for" someone don't neatly map into "support for" everybody in his
party. I'd say the obvious generalized criterion is mono-add-plump (i.e.
if you only use your first preference, then whoever you vote for
shouldn't be harmed), which I'd say that most sensible methods should
pass; but I don't think it's necessary.

So to sum up, I think proportional methods have to pass your condition
in the "party list, each voter chooses one party" case.

-km

Thank you, I was primarily interested in the "party list, each voter chooses
one party" case.

LB

---------- Původní e-mail ----------
Od: Kristofer Munsterhjelm km_elmet@t-online.de
Komu: Luděk Belán LudekBelan@seznam.cz
Kopie: election-methods@electorama.com
Datum: 28. 8. 2023 18:39:06
Předmět: Re: [EM] Definition of proportional electoral system
"On 2023-08-28 13:46, Luděk Belán wrote:

It might be, for quota-based proportional representation.

The Droop proportionality criterion says that if a solid coalition (in
this case, a party) obtains more than 1/(n+1) of the vote, it should get
at least 1/n of the seats.

So if we have two parties for two seats, and one party has more than 33%
of the vote, then it must get at least one seat. Then the other party
also has more than 33% and must get the other seat. So there's no room
for nonmonotonicity in the mono-add-plump sense (i.e. additional votes
for A won't harm A).

For things that generalize Webster and other divisor methods, it's even
easier: the party list case is just Webster (or D'Hondt or etc.), which
themselves are monotone functions and so pass your condition.

Things get a lot messier for ranked voting methods, though, because
"votes for" someone don't neatly map into "support for" everybody in his
party. I'd say the obvious generalized criterion is mono-add-plump (i.e.
if you only use your first preference, then whoever you vote for
shouldn't be harmed), which I'd say that most sensible methods should
pass; but I don't think it's necessary.

So to sum up, I think proportional methods have to pass your condition
in the "party list, each voter chooses one party" case.

-km
"