Matthew Yglesias, back from blogging haitus, briefly looks at Shinui's possible role in an Israeli coalition government. The case of Israel's 120-member unicameral parliament, the Knesset, is particularly interesting because of its abnormally high number of political parties — 13 parties received Knesset seats in the January 2003 election because they received over 1.5% of the popular vote. (The Knesset uses pure proportional representation within one, nationwide district.) Leaving aside the question of why such a low threshold was chosen — Israel's is the lowest in the world — the large degree of fragmentation leads to serious barriers to coalition formation.

Michael Laver and Norman Schofield's Multiparty Government discusses this problem, although it mainly concentrates on European countries where the major parties are larger. In the most recent Israeli election, by contrast, no party received more than 30% of the total vote, and the Likud only received 38 seats — 23 seats short of a Knesset majority. This makes coalition formation particularly problematic because no single party can provide an overall majority — even a coalition with second-place Labor, with 19 seats, is too small to win an investiture vote (Israel's laws require a Knesset majority to vote in favor of forming a coalition, which makes a minority government exceedingly unlikely). So, what sorts of coalitions are possible?

Some theories suggest that the most likely coalitions to form are “minimal winning” coalitions — coalitions that involve the least number of parties while still gaining a majority of seats; i.e., where the loss of one party would make the coalition a minority. William Riker goes further to predict that the most likely coalitions to form are “minimum winning” (or bare majority) coalitions: ones that produce the smallest possible majority. Looking at the incoming Knesset, the following 3-member minimal winning coalitions are possible:

• Likud + Labor + Torah Judaism (62)

• Likud + Labor + NRP (63)

• Likud + Labor + Meretz (63)

• Likud + Labor + National Unity (64)

• Likud + Shinui + Shas (64)

• Likud + Shas + Labor (68)

• Likud + Labor + Shinui (72)

There are actually 3,615 possible minimal winning coalitions (out of 4,044 possible majority coalitions, most of which, unsurprisingly, involve the Likud). Furthermore, there are 92 minimum winning coalitions, with the coalition holding 61 seats; most of them involve large numbers of parties. The smallest minimum winning coalitions involve 4 parties:

• Likud + Labor + Yisrael Ba'aliya + United Arab List

• Likud + Shas + Meretz + NRP

• Likud + Shas + National Unity + Torah Judaism

• Likud + Shinui + Meretz + United Arab List

• Likud + Shinui + Meretz + Yisrael Ba'aliya

• Likud + Shinui + NRP + United Arab List

• Likud + Shinui + NRP + Yisrael Ba'aliya

• Likud + Shinui + Torah Judaism + Am Ehad

• Likud + Shinui + Torah Judaism + Balad

• Likud + Shinui + Torah Judaism + Hadash

However, from a policy standpoint, few of these coalitions make much sense; Arab parties (Balad and UAL) aren't going to be part of a Likud coalition, and neither is the communist Hadash. Meretz is unlikely to join with Shas and the NRP. The only coalition here that seems remotely plausible from a policy standpoint is Likud + Shas + National Unity + Torah Judaism.

A 61-seat coalition is unlikely simply because of the instability of the parties in general; Sharon probably wants a strong coalition that can withstand a few dissident members (despite the plethora of Israeli parties, party discipline is relatively low). This suggests a policy-based coalition involving the larger parties, to reduce the number of parties involved and the risk.

The “ideal” coalition for this task would be the widely-mooted Likud + Labor + Shinui coalition, which with 72 seats is the largest possible three-party coalition (and which might accrete some additional members from the smaller parties). However, widespread reports that Labor is not willing to join a Likud coalition leave only a Likud + Shinui + Shas three-party coalition, with a more tenuous 64 seats and serious policy differences (Shinui's support is attributed to opposition to excessive patronage to the ultra-Orthodox; Shas is the largest ultra-Orthodox party). Therefore, other possibilities may be considered:

• One option would be a minority coalition, with Likud + Shinui in the government but with investiture support from Labor. This could allow Labor to keep its promise to stay out of a coalition without necessitating a new election (or a more right-wing coalition).

• Likud + Shinui + Yisrael Ba'aliya, with support from some defectors from Labor.

• Likud and Shinui could cobble together a coalition with some of the religious parties (with or without Meretz). Alisa suggests that Shinui is fairly open to working with most of the religious parties, barring Shas.

• Finally, Likud could fail to form a government, presumably leaving Labor, Shinui, and Meretz to try to cobble together a coalition involving the Arab parties and the Am Ehad (One Nation).

The bottom line: throw the coalition theories out the window when it comes to Israel — at least until they get a sensible threshold on the books.

Ha'aretz has a page with some charts showing some possible alternatives (thanks to The Talking Dog for the link).

Noah Millman, Michael Pine, JB Armstrong, and SharkBlog have some interesting coverage as well.

My theory: Likud + Shinui + Yisrael Ba'aliya + NRP, with either a lot of Labor defectors (probably to Shinui or a new group) or a new Labor leadership.