Israeli Elections: D'Hondt vs Sainte Lague Explained
Re-posted from Roseanne World Old Forum:
http://www.roseanneworld.com/forum/view ... 4971#74971
http://usparliament.org/
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Israeli D'Hondt parliament seat distribution system:

Currently there are 120 seats in the Knesset and the Israeli government requires the threshold of 2% for a party or independent to win one of the 120 seats.

This results in a maximum satisfaction level of 50%, minus 60 votes, of the votes that were cast to elect the government made up of 120 MPs.

If there are sixty new innovative parties and independents who all garnered exactly 2% of the votes in the election, then they are all elected with 100% of the votes.

Only 1/2 of the seats (60) can be elected with a threshold of 2% (2% of 100% is 2 and 2% of 120 is 2.4 and 2.4 x 50 is sixty seats elected), so the remaining 60 names must be elected somehow to fill the parliament, and can be elected with a minimum of one vote each.

So take away 60 votes from the 50% (60 MPs) elected, to guarantee the election of the remaining 60 seats. Total maximum guaranteed satisfaction level is 50% of the total votes cast, minus sixty votes when there are 60 innovative parties and independents who garner the minimum 2% required.

Any other combination results in a lower satisfaction level.
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USA Parliament's Sainte-Lague parliament seat distribution system:

Should the Israeli government use pure proportional representation under the USA Parliament's Sainte-Lague parliament seat distribution system, then the satisfaction level is guaranteed to be much higher, 92.12% plus 120 votes.

The way it works, is you divide the total number of votes cast by the closest way to a 121-way tie (1/121ths or .826%), so the first 120 names that break the tie with one more vote are elected.

Last preference #121 does not get plus "one vote" and so #121 does not get elected.

Total votes cast / 121 = .826% of the total votes. So the threshold is .826 (or 1/121th) plus one vote. (.826 plus one vote) x 120 seats = 92.12% plus 120 votes.

So the total minimum satisfaction level is 92.12% plus 120 votes, the total guaranteed minimum number of votes which elects the government under the Sainte-Lague system, elected to the Israeli Knesset whether there is 60 innovative new parties and independents or any number/combination of parties and independents.

92.12% plus 120 votes total satisfaction is a much bigger satisfaction level than 50% minus 60 votes, a difference of 42.12% plus 60 more people would be satisfied with the results because their vote actually elected a name.

Varying combinations of numbers of votes cast under this system will result in a highers satisfaction level, i.e. numbers of votes that count to elect a name.
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The 8th USA Parliament will elect up to 1000 names in 2012 under the Sainte-Lague parliament seat distribution system, with a guaranteed satisfaction level of .999% plus up to 1000 votes.

If anyone can comment on what I wrote, I'd like to hear how I can explain this better, of any other comments too.