Some have idea that there is such a thing as effective thresholds in elections. They say with ten people to be elected, there is an effective threshold of one-tenth of valid voes, so 10 percent. But this seems only applicable if no votes are wasted and if the votes are equally distributed among winners, which is not the case often.
This might be thought to apply to PR but it implies to any multiple-member districts. Party-list proportional and MMP (as usually envisioned - leaving out Denmark's MMP system) do not have MMDs, so those people seem to be talking about district-level PR systems, such as STV or SNTV or perhaps a regionalized form of Additional Member System (regional party-list, and even then only ones where votes are transferred to prevent waste (STV).
In transferable vote systems, surplus votes (votes more than the assumed threshold such as 10 percent) do not rest with the winner but instead are transferred away. There you do find that each winner in a ten-seat district has about 10 percent.
But in any system where votes are not transferable, you find wildly varying numbers of votes received by winners and also many votes wasted.
for example, in real-life Vanuatu's last election
held using Single Non-Transferable Voting,
in Malekula, a 7-seat district,
while you might think that the effective threshold was 14 percent (100 divided by 7), the reality is much different. (And this is not due to influence of party tallies - candidate vote tallies are the only things considered in SNTV - not party totals or other such.)
Winners in Malekula all took less than 14 percent -
they took a range of votes from 7.46 percent to 5.17 percent.
Only 42.47 percent of the votes were used to elect someone.
However if you look at the number of voters who saw at least one member elected for the party of their choice, you see more general satisfaction.
Candidate(s) of five different parties were elected.
About 33-40 percent of voters did not see any one of their preferred party elected.
60 percent or more of the voters did see someone elected that they party-wise agreed with.
And that is likely considered a fair result, satisfactory to most voters
Where votes are not transferred to scientifically ensure that each party gets the number of seats that they are due proportionally, the "effective threshold" does not hold much power.
Under a system that uses transferable votes, the effective threshold based on the total votes divided by seats might be more useful not as a minimum but as a "quota" to predict or determine how many seats each party should get.
The idea of a scientifically-derived effective threshold where votes are not transferred reminds me of people saying that in FPTP a winner must have a majority of the votes.
There is actually much waste and luck in elections where there is no restraint on a single group (perhaps a minority) taking all the seats.
Fairness/general satisfaction depends on
at minimum, single voting in multi-member districts (SNTV)
or to produce more proportionality, a scientific method of allocating seats,
such as:
single-voting/transferable votes/quota to prevent waste through surplus votes staying with winners (STV)
or party-list PR where multiple seats are filled in accordance with the will of a pool of voters (whether in party-list PR or as top-up seats in MMP)
or single voting/party votes/transferable votes as in a party-list or top-up in MMP system where there are back-up preferences to prevent waste and increase the portion of effective votes.
Single-winner elections with non-transferable votes do not produce fair representation, as I'm sure we all agree.
The more we get away from that, the more proportional it is.
Hare envisioned STV applied to Britain seeing one country-wide district with each voter casting just one (transferable) vote.
No local representation produced thereby except through the mechanism of the quota - if an area had the quota and each voter marked their first and back-up preferences only for candidates from that area, one of them would be elected and there was nothing anyone elsewhere in the country could do about it.
But without that discipline (which would have to cross party lines in some cases) there would be no guaranteed local representation.
City-wide districts (or regions) electing multiple members allow both local (city-scale) representation and supporters of multiple parties to be represented therein, whether through STV or SNTV or regional MMP/AMS.
Without transferable votes, some votes will be wasted but the general satisfaction and votes represented will be high.
With transferable votes, even with just one back-up preference, the portion of effective votes will increase with positive effect on proportionality of the elected result.
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More on the use of multiple-member districts in most PR systems
The idea of an "effective threshold" (as derived by dividing overall votes by number of seats) - 10 percent in ten-seat district - doesn't hold up if you look at real-life elections.
For one, there are some PR systems that do not use MM districts, especially a ten-seat district.
New Zealand (MMP) does not have MMDs, except for nation-wide top-up.
Party-list PR in most cases does have districts, except for a few examples.
Only Netherlands and Israel and a few others use atlarge districitng. (unless you mean it has one MM district - the overall pooling of votes to allocate seats, in which case ten is far too low a number for the number of members elected there).
REgonalized AMS uses regions that I suppose could be considered MM districts.
Election of members of the Scottish Assembly is one instance of this. In each region, seven top-up seats are added to the victors in 8 to 10 district seats, in compensatory manner. Note the number of ten seats is not used in any of these regions. Region seat numbers range from 15 to 17.
But for interest sake, we see that Greens won a seat in Mid Scotland region with 7.4 percent of the vote.
MMP almost never uses MM districts (unless you mean it uses one - the overall pooling of votes to allocate multiple top-up seats which are multiple, but in which case ten is far too low a number).
Denmark is only mixed-member PR system that I know of that uses MM districts.
North Zealand (a district in Denmark) is the only district in Denmark that elects ten members. (Perhaps it is the only district in the world that elects ten members under MMP.)
There in 2019, the Socialist Peoples Party got 6.9 percent of the vote and took one seat.
This is not expected if effective threshold is 10 percent, and it happened despite party tallies being used to allocate seats.
As I point out above, such a thing is due to votes being wasted as happens under any system where votes are not transferable, whether it is party-list/MMP or single-winner FPTP.
Under other PR systems or semi-proportional systems where MM districts are used, such as Vanuatu's SNTV, seats are not allocated based on party tallies. Votes are wasted, and also party tallies are mal-distributed among multiple candidates. There too you cannot simply divide the overall vote tally by the number of seats to get an "effective threshold" that will determine which party will have candidate(s) elected and which will not.
Without transferable votes and the high rate of effective votes that it produces, "effective threshold" is not a hard and fast formula to determine election or defeat, or it is much lower than the 10 percent in a ten-seat district that some might be saying.
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It is like this
Proportionality is produced by balanced, mixed election of members in multi-member districts or in some other pooling of votes.
"Pure" Party-list PR does not use districts. It usually produce proportionality by allocating seats in accordance to overall party vote tallies.
Under some party-list PR systems, there are divisions of the electorate (in provinces or states) that elect multiple members based on party vote tallies. These systems could be said to have multi-member districts. In each "district", proportionality is produced by allocating seats in accordance to party vote tallies within the state or province.
Mixed Member Proportional (MMP) uses districts but in almost all MMP systems the districts are not multiple-member districts. Each elects only a single member. Proportionality is produced by allocating top-up seats based on overall party vote tallies. This is done in compensatory manner in response to the way that the district seats were filled (and sometimes the top-up seats are actually based on different votes than are used to fill the district seats).
Regionalized Additional Member System, which is regional-level party-list PR, use single-member districts and to get proportionality, elects other members by grouping those districts into regions that elect top-up (multiple members based on party vote tallies in compensatory manner in response to the way district seats were filled and sometimes the top-up seats are actually based on different votes than are used to fill the district seats).
The only MMP system that uses multi-member districts is Denmark where members are elected by party vote tallies in the MM districts and top-up members are elected based on overall party-list tallies.
Denmark is not the only country to use multi-member districts.
There are other countries that produce balanced, mixed election of members in multi-member districts. They do this by use of STV or SNTV at the district-level.
Countries that use STV or SNTV use multi-member districts that elect balanced mixed representation in each district. This ensures that, both at the district level and overall, representation is mixed and parties have roughly balanced, fair representation
Under STV, MM districts are used in Ireland and Malta and Australia for Senate elections.
Under SNTV, MM districts are used in Vanuatu elections and some other places. Votes are not transferred so perhaps a third of votes or more are wasted in each district.
Under STV, votes are transferred to ensure parties get fair representation by preventing successful candidates retaining more votes than needed to win and also to prevent waste of votes by ensuring that about 80 percent of voters see their vote used to elect someone.
Both of these systems use Single voting - where each voter casts just one vote in a MM district. This alone prevents one party from taking all the seats in the district.
There are systems where voters can cast as many votes as the number of seats to fill. These systems use MM districts but usually they do not have PR.
Some of these systems, such as Block Voting, operate in such a way that a single party or group can take all the seats in the district. This is not PR.
Block voting uses MM districts but it is not PR. It is used in many city elections in Canada and in elections in other countries.
In systems where a voter can lump all his or her votes on a single candidate (Cumulative Voting), if enough do that, minority representation may be produced. So under the right conditions CV produces district-level PR.
Cumulative Voting is used in some city elections in the U.S.
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