Shas and Shinui Knesset Parties as the Lotka-Volterra equation

The demise of Shinui party in the last Israeli parliamentary elections (March 2006), made me realize that Shas and Shinui should probably follow the Lotka-Volterra equation. As I explain below, the problems are not totally equivalent for several reasons. Nonetheless, many of the L-V elements exist in the Shas/Shinui pray/predator system… The equivalency is given in the following table:

Equivalency Table:

Lotka-Volterra	Shas / Shinui
Prey (e.g., Rabbits)	Shas
Predator (e.g., Foxes)	Shinui
Prey's Food (e.g., grass)	Government Money

Before I explain myself, some background is in order for those unfamiliar with either the Israeli Parliament (aka the “Knesset”), or the Lotka-Volettera equations, or both (though if you don’t know either, I suppose you wont find this blog entry too amusing). Skip the blocks if you are familiar with both.

What are Shas and Shinui? For those unfamiliar with the Knesset, Shas is a religious party supported by Orthodox Sephardic voters (unlike the secular community, the ultra-religious community is very sectorial [racist?], separated to Ashkenazi and Sephardic jews, and many other subdivisions). Shas tries to better the conditions of social parasites, including Torah students who don't work at all or low social class families with n>>1 kids whom they cannot support. (Don't get me wrong, I have nothing against bible studies nor am I against socialism, a society should take care of those who are unfortunate and cannot support themselves [unlike the USA!]. There is however no reason to provide incentives not to work, if you are able to, or incentives to have many kids you cannot support). On the opposite end is Shinui. It was once said that the problem in israel is that a third of the population works, a third pays taxes, and a third does military reserve service, and the problem is that it is the same third. Shinui tries to help this third. To a large extent, this is done by fighting the large fractions of the population which avoid working, paying taxes or serving in the army, hence the conflict with Shas.

What are the Lotka-Volterra equations? The L-V equations are a pair of first order nonlinear differential equations which describe how a prey-predator system (i.e., two species) interact. They were independently proposed by Lotka and Volterra around 1925. The equation for the prey includes natural growth (i.e., assuming unlimited resources) and their decline by the predator population. The predator's equation describes growth depending on the amount of food available, i.e., the amount of pray, and natural death. This nonlinear set of equations leads to a periodic oscillation. This can be seen, for example, in the long stretch of lynx and hare data recorded by the Hudson Bay Company (which incidentally, is the oldest company in North America, still to operate... at least, I find it bizarre that an ordinary dept store actually has a rich history which began in 1670 and included the control over more than half of what is now modern Canada).

Just by reading the intro boxes, you may already see why I find the two supposedly different “systems” actually quite similar. The Shas/Shinui behavior is that of a predator/pray system.

Shas lives on money it tries to get from the government, whether it be for Religious Torah students (who don’t work) or for more social benefits (so that a family of 8 could live off of welfare without having to work at all). If in power, they simply grow unhindered like rabbits or hares.

Shinui on the other hand, live off the success of Shas, their pray. When shas does better, and grows, the resentment in the general secular population rises, and the power of Shinui rises as well. When they become large enough, they replace Shas in the coalition government, cut the funding for Shas, and their size quickly shrinks. Once the prey, i.e., Shas, decreases sufficiently, Shinui loses its power (as it is not needed anymore), thereby allowing shas to enter the coalition government, obtain funding and grow… i.e., the same cyclic behavior as the Lotka-Volterra dynamics.

Of course, there are a few interesting differences between the two systems. First, the political system has discrete time steps, in the form of elections. The L-V is continuous. Second, the political system has both discrete states and continuous states (whether a given party is in the coalition or not, and the number of MKs [Knesset Members]). The natural prey/predator populations are continuous. Both systems are affected by outside influences (e.g., weather on L-V), but those on the Political one are very large (e.g., economic situation, security conditions, etc). If I had the time, I would actually try to model it quantitatively… but I don’t have.

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