[EM] Challenge: two-party methods

[Kristofer Munsterhjelm]

Juho Laatu wrote:
> After some recent discussions and thoughts around two-party systems I
> thought it would be interesting to discuss two-party systems also in
> a more positive spirit. The assumption is thus that we want the
> system to be two-party oriented. We want to have two strong parties,
> and one of them should rule. We want to allow only well established
> parties with wide support to rule. The first obvious approach is to
> ban all other parties than the two leading parties. But maybe we
> don't want  to be so brutal. Let's not ban the possibly already
> existing, much liked and hopeful third parties. It is also good to
> have some competition in the system. Let's not allow the two leading
> parties think that they don't have to care about the voters and they
> can do whatever they want, and stay in power forever.
> 
> What would be a good such method? In addition to what was already
> said we surely want e.g. to avoid the classical spoiler problems.

I can think of two simple PR-based methods.

In the first, you use ordinary divisor-based PR, but set the divisors so 
that they have a great large-party bias (even worse than D'Hondt).

In the second, you also use ordinary divisor-based PR, but top up the 
list of the largest party so that it always gets 50%+1 of the seats if 
it would otherwise get below that.

But I think that any two-party system will discourage smaller parties. 
If only the two major parties can rule, voters will strategically think 
that "either I can use my vote to grant the lesser evil more seats/power 
so it can defeat the greater evil, or I can use my vote to vote for a 
small party that hasn't got a chance beyond being the opposition anyway. 
I'll do the former". That sort of thinking will create an invisible 
barrier to third parties, because as long as the third parties aren't 
large enough that they might win (become one of the top two) with a 
small amount of additional votes, voters won't vote for them, and if 
they don't vote for them, they'll never get close enough to the threshold.

I can think of two ways to get around that, but both would bend the 
definition of a two-party system.

Let's call the first an "explicit coalition system". The election 
process itself is party list PR. After the election is done, a group of 
parties with a total vote share greater than a majority must form a 
coalition; they do so by an internal supermajority vote, after which 
this group gets the government and the rest becomes the opposition.
After that is done, they rule until at least one of the parties (or some 
fraction of the whole group), plus the opposition (or supermajority 
thereof), agrees to dissolve the current coalition. After that is done, 
there are new elections. The current coalition rules until the next 
coalition can organize itself.

The second, I'd call "PR by credit". Again, votes are counted as in 
party list. Each party also has an "account". After the election, the 
number of votes for each party is added to the relevant party's account. 
Then the parties allocate votes to gain seats in a continuous bidding 
process. That is, call parties 1...n's current bids, B_1...B_n. Then the 
tentative seats allocation is according to some major-party biased 
divisor method that considers B_1...B_n the number of votes each party 
got. The seats count is updated continuously until the timeout, then 
each party's bid is withdrawn from its account. While it is unfair in 
any given election, the smaller parties can accumulate votes in their 
accounts and later use this to take the throne of government, if for 
only a term.
However, I think this kind of hybrid monetary system would have some 
adverse results. First, it would cause great oscillations. The 
composition of the parliament could swing hard left, with lots of, say, 
environmental bills, then swing hard right, with the new government 
scrambling to undo those bills and to impose their own, then swing hard 
left again, each sweep of the pendulum causing chaos. Second, 
differences in turnout could add more noise: if there's less turnout, 
there's less of an impact to each party's account.

> P.S. Could there be also three-party or n-party systems? Limiting the
> number of parties to n would be an alternative to thresholds. This
> approach could be used also in a two-party system, i.e. set the
> threshold e.g. to 33% (or lower, or higher). Does the proposed method
> work better than such thresholds or simply picking two largest
> parties?

The approaches above could be adjusted to n-party systems, yes.