Your idea of having one vote that functions as both a party vote and an electorate vote is a possibility I wrote an honours essay on in 2000. I concluded that it could be worthwhile for preventing people from creating an overhang to make their vote count twice, but I couldn’t find any historical evidence of this happening. When the Maori Party got an overhang in 2005, I realised its relationship with Labour could easily develop into the sort of thing I envisaged might need to be stopped by introducing a 1-vote MMP system. I’m still not sure if it is going down that road.

The other argument I identified for the 1-vote system was that under two-vote MMP you can vote for an electorate MP from a party you oppose, and you could use that power to weaken the party you oppose by electing an MP who was either incompetent or likely to cross the floor, and that person comes out of the party’s seat allocation. Whether that situation can develop in practice depends on the parties’ candidate selection processes.

One compromise between having no threshold and having a threshold that disenfranchises voters is to have a preferential system for the party vote. This means you list parties in order of preference, but if your first preference party is below the threshold, your vote goes to your second preference party. Of course, if you were confident of your first preference party passing the threshold, you wouldn’t need to even choose a second preference, so it wouldn’t be a lot more work for voters.

I have wondered about the idea of adding extra seats to preserve proportionality in the event of an overhang (but I didn’t know they had it in germany – I thought it was just my own idea). Presumably it would work on the idea that it removes the incentive to create an overhang, so people wouldn’t bother doing it. But you could still accidentally get a dodgy situation where Anderton wins his electorate but only gets one fifth of the number of party votes needed for a seat, so parliament balloons from 120 seats to 600 seats. That’s a silly enough possibility that we shouldn’t do it.

In Germany it’s 5% or 3 electorate seats for State elections, although you’re looking at 598 seats in total (with overhangs of 15-20 seats not being unusual). Their mix is considerably more complex than ours though in that the electoral votes are FPP while the party vote is MMP.

and of course they have a bicameral system.

northpaw – also intriguing. With the added value of simplicity (or at least it seems simple to me, so I’m assuming voters would understand it clearly).

Damn, this has got me even more excited about the propects of a proper review of MMP. If only we’d had a more flexible process than the one that brought us MMP, where we were presented with a choice of ready-made systems and asked to pick.

Off-the-rack is rarely as elegant as tailor-made.

In the case of the Maori Party here, we would end up with a parliament of over 200 members… I don’t see that being acceptable to anyone.

Israel’s electoral system for the Knesset has one electoral district with a 2% threshold, but they have separate a ballot for Prime Minister – which seems to me a silly aspect which we shouldn’t adopt: how would Helen Clark cope as PM with a right wing majority on he House? Or vice versa?

‘Say a 2.4 million votes are cast for 120 seats. One party gets 1.2 million, another 1,190,000 and a third 10,000. Surely St Lague wouldn’t have a party with less than half a percent of votes taking a seat away from one of the big ones.’

And you/Graeme replied:

‘I can’t see a problem with this…… The question basically is:
which is the more proportional Parliament?
*the one where Party A gets 60 seats and Party B gets 60 seats, or
*the one where Party A gets 60 seats, Party B gets 59 seats and Party C gets 1 seat
Sainte-Lague says the latter option, and standard indices of disproportionality would agree.’

But that’s false. In the case sketched Party B and Party C have the same 120th St.L quotient,10000. The preference for 60:59:1 allocation over a 60:60:0 allocation is settled by whatever policy one has for breaking ties, and not by St L. itself.

And then you/Graeme suggested that St.L expresses the idea that a small party’s fractional seat shares have more right to be honored than large parties fractions.

But that’s false. Once things are in seats÷votes terms, St.L plays an absolutely straight bat: all fractional entitlements are treated the same way, and no special consideration is given to small parties’ fractions. St.L. is, in fact, the only series-of-divisors rule that is so nicely neutral – that’s a principal reason to use it.

The only point that was needed in the original discussion was the simpler one that half a seat quota often ends up being the effective threshold under St.L.. No judgment about big parties’ half seats vs. small parties’ half seats should have been entered. Sorry to be pedantic. If it wasn’t someone who’s normally v. reliable and careful making the mistake, I wouldn’t bother insisting on the clarification/correction!

The first party’s 41st St.L. quotient is then 4.988, i.e., > 4. The party with .4% of the vote doesn’t get its first seat unless parliament expands to at least 51 or 52 seats (depending on how ties are handled)

More generally, Graeme’s ’100% lack of representation shock! horror!’ reasoning does not correspond to St.L. at all: St.L is unbiased between small and large parties, and in two party cases it always agrees with the ’round exact seat shares to nearest integers’ algorithm.(Theorems are available in the usual places) So if you think it’s shocking for a 40.6 exact seats party to get the 41st whole seat (because the 40.6 party will benefit ‘so little’ and the .4 party ‘loses so much’), well, get over it. If parliament has a million+1 seats, then a million+.6 seat-earning party gets all the seats and the .4 seat party none. O the humanity.

St.L. *does* minimize the voter-weighted (squares of) [(allocated seats)÷(party votes)] [total seats÷total votes]. That was the key result of the original 1910 paper. But that doesn’t correspond to Graeme’s gloss – in effect voter-weighted degrees of over-representation in possible allocations are also considered (hence the lack of bias).

St.L’s mathematics benefits small parties on some occasions but helps large parties on others. In 2005 Labour was entitled to (something like) 49.95 seats and got 50. Fine. But if 2000 Maori party voters had spread their party votes evenly between, say, the Progressives and NZ First, and 120 Green voters had voted for Labour, and everything else had stayed the same, then Labour would have been entitled to 49.98 seats but St.L would have given Labour a 51st seat, ’rounding’ 49.98 up to 51. Woo hoo.

Candidates stand in electorates for their parties. Yes, I know they do so now, but now if an electorate candidate loses all votes in support are lost, too. A lot more efficient would be to fuse the two – party and electorate. One tick, not two, as you infer. Yet winner takes the individual electorate ‘seat’ and all votes count towards a national majority (or sum as determined by participating parties). If that’s clearer and/or the same as you describe then so be it..

And that the extra MPs would be chosen from a list, still?

Yes, something suitable to the parties who, with their ‘seat’ winners must allocate according to needs per the summed votes.

Do you happen to know how parties in the Netherlands and Israel rank their lists, in that case? Is it, as the Greens (and Greens alone) do in NZ and give every member a vote, or some other way?

Our mayoral elections certainly aren’t proportional (each city only gets one mayor), but DHB and council elections are. Yes, the person who gets the most 1′s usually gets elected, but a bunch of other people get elected too – and not always those who would have been elected based on 1′s (e.g. my council ward saw Jack Ruben miss out on a seat).