Tuesday, February 21, 2012

Examples proving the mathematical necessity of the Supermajority in specific situations:

This post provides mathematical examples proving why/when a supermajority is necessary. It expands on the basic explanation of supermajority requirements here and uses property levy examples (which are a type of vote that needs a supermajority).

A supermajority vote is necessary anytime you allow a subset group of people to vote on a matter that's beneficial to them but they don't pay for.
--Abbreviations used: Levy Payer (LP), Non-Levy Payer (NLP)
--Colors (occasionally used): Blue for LP items /Red for NLP items
--Assumptions used: 100 people vote

1) If all 100 voters are LPs: The vote should require 51 votes to pass (The basic Simple Majority).

2) However, if the 100 are split we discover that the vote needs to be a supermajority. Here's why (using 55 LPs & 45 NLPs):
To get the simple majority of LPs you need at least 28/55 of them. The problem is that with the introduction of the 45 NLPs voters, you've created a flawed vote. Flawed because you could get passage with 5 LPs (a far cry from the 28) and 45 NLPs voting yes (5+45=50). That would be passing a tax with only 9% (5/55) support from the LPs who'd actually pay the tax! If NLPs voted yes by 85% (.85x45=38), the levy could still pass with a meager approval rate from LPs of 21% (.21x55=12)...(38+12=50).

Obviously a 100% (45/45) NLP voting rate is extreme, and 85% would be quite high, but the mere fact it's a possibility shows the flaw. However, a very realistic 75% (34/45) of NLPs would cause passage with a mere 31%(17/55) LPs approval rate (still extremely unfair). Obviously, passing a tax on people, when only 31% approved it, is a flawed system. By no means is that an "extreme" example. High approval rates are much more common among people who benefit from, but don't pay for, something. Even using 65% (29/45) NLPs you find that "a minority" 38% (21/55) of LPs still results in the tax being passed upon them. How could anyone support a belief that it's ok to pass a tax on people when only 38% of them actually voted for it? How could that be seen as fair/democratic?

3) How about this: If Washington was having a vote to increase the sales tax to 12% you surely would not want people from Idaho/Oregon allowed to vote on it. If they "were" allowed to participate, you'd want a "supermajority vote" because, as stated above, you'd be adding a subset of voters who wouldn't pay the extra tax but would benefit nonetheless (as people crossed the border to avoid the increase). Wouldn't you be a little upset if that 12% tax passed with only 21-38% support of actual WA state voters? Would you think that was "democratic"...? Remember, the mere fact that it's possible shows the flaw (and these aren't even unrealistic voting figures).

4) To correct this problem: Using the same 100 people example, you start by accounting for the baseline premise of wanting at least a 50% (simple majority) approval rate among the actual "LPs" (WA residents in above example) who pay the tax (.5x55=28). Now, you simply make an educated estimate of the "NLP" yes voting rate. Again, a higher yes rate is perfectly logical/normal when people vote for something they benefit from but don't pay for (especially with all the exploitative "for the kids" ads)... Using the 75% rate (from above) we get (.75x45=34). Adding 28+34 yields 62 votes required (a supermajority 62%). The worst case scenario of 45 NLPs voting yes results in 28+45=73% required to pass with at least a "simple majority" of 28 LPs.

Even though 60% is less than the above 62% & 73% figures it still represents a good all around happy medium figure to be used in these types of situations (subset introduced into equation) and it's a heck of a lot better than the simple majority rule that was swindled in 2007's HJR4204 (passing w/less than 1% of vote). A vote that most likely wouldn't have passed if people had a better understanding of the mathematical reasons necessitating a supermajority...

Again, it's basic mathematics that shows why a supermajority vote is required in order to simply even out the vote and account for the addition of a group of voters who don't have to pay for the very thing they're voting for.

****If a levy passes by 60% there's a good chance it would've also passed with a simple majority vote consisting of only LPs (demonstrated by the 28 in above paragraph). Therefore, the tax could be seen as resulting from a legitimate vote. However, any that pass with less than a supermajority are mathematically flawed voting results. It's quite different from being seen as emotionally flawed when an item someone favor fails.

The solutions are either:
1) Requiring a 60% Super Majority to pass property tax issues
2) Allowing only levy payers to vote on those measures...
3) A sales tax with total revenue evenly distributed on a per student basis would be a much more equitable solution (everyone pays in) and would also remove the disadvantage that can occur in lower property value school districts. Net-net the schools would still get their money, but in a much more fair way.

5) There's an inherent conundrum for people in addressing an issue that benefits them but is factually flawed (especially when fixing it could be disadvantageous to them). Which one takes priority, personal benefit or truth & correctness?... The benefit a simple majority provides of aiding in the achievement of a desired result (levy passage), does not change the "mathematically indisputable fact" that it's a flawed process irt basic fairness and democracy. So again, which takes priority, personal benefit or truth & correctness?...

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