I forgot to mention this in the "Mixed Heritage" article, and I feel it is a little too important to be added there as a comment:
In a proportional system, if the percentage of the vote backing the president drops too near 50%, small interest groups have incredible amounts of pull in the coalition. If a president has 51% of the vote and a group represents 2% of the population, they can make unreasonable demands and have them met, so long as the president wishes to retain his post.
Since in Israel, at least, government posts offer immunity to criminal prosecution (it can be voted out, but it's tough), and since (as aforementioned) corruption tends to be a problem in proportional systems, it is very *likely* that the president wants to hold onto power at almost any cost.
This is actually the chief reason why I am not the biggest fan of proportional systems, and why I would never suggest that the U.S. should adopt Israel's system. Components of that system are clever, but the consequences sometimes outweigh the benefits.