Tuesday, October 25, 2016

Why Illegal Votes Matter (As If You Didn’t Already Know)

     Voting power analysis fascinates me, in part because among all the branches of finite mathematics it’s the one that’s most dependent upon timing effects. Simple, static voting power problems are interesting enough. Here’s a typical case:

     Let the aggregate voting power of a committee be set at 1. Imagine a committee of four persons. Add the condition that the committee has a Chairman with the power to decide the results of a tie. What is the Chairman’s voting power, and what is the voting power of any other committee member?

     I’ll save you the analysis: the Chairman will get his way seven-eights of the time, as all three of the other members must vote against him to thwart him. Therefore, the Chairman’s voting power – i.e., the fraction of cases in which his vote will determine the outcome – is 7/8; any other member will possess one-third of what remains: (1/8)*(1/3) or 0.0417 (rounded to the nearest ten-thousandth). Clearly, “it’s good to be the Chairman.”

     But the really interesting problems in voting power are time-dependent. Many depend upon an elusive, sometimes partly illusory consideration called “lock-in.” The following is a typical example.

     Let there be a committee of five persons – once again, aggregate voting power 1 – who have a delimited but non-instantaneous time period over which to vote on some issue. At the very beginning of the process – i.e., before any votes have been cast – each member has a voting power of 1/5 (0.200). Stipulate that a vote once cast is locked in: i.e., it cannot be changed. After four votes have been cast, what is the voting power of the remaining member (before the interval expires, of course)?

     This is a slightly more difficult calculation than with the committee of four. To cut to the chase, there are only the following ways four persons can vote:

  • Four unanimous, either yes or no;
  • Three in agreement, one in dissent;
  • Two against two;

     Those configurations cover thirty of the thirty-two possible configurations of the potential votes. (If this seems elusive, compare it to the number of values a five-bit number can represent.) However, in only one set of configurations does the “holdout” vote determine the outcome: the two-against-two set, which are six in number:

  • YES YES no no
  • YES no YES no
  • YES no no YES
  • no YES YES no
  • no YES no YES
  • no no YES YES

     Since 6*(1/30) == 1/5 (0.200), it would seem that the “holdout’s” voting power is unaffected by his decision to withhold his vote till the last moment...if we omit the possibility of influence.

     The holdout on the committee-of-five above could be a “disinterested patriot,” or he could be “out for whatever he can get.” However, even the most purely civic-minded citizen can be influenced by persons eager to have his support. In a political order such as ours, you may rest assured that those with something to offer him will bid for it.

     As I’ve written before, contemporary politics is largely driven by the desire to enlist voting blocs: identifiable groups, bonded by a common interest, whose voters can be swayed to one or the other party because of that common interest. An excellent example of this is the National Rifle Association, which will never, ever side with an anti-gun-rights candidate (usually the Democrat). On the other side of the scale we have the Sierra Club, whose allegiants normally vote for the Democrat as the “more environmentally friendly” of the two candidates. There are many similar cases.

     However, the less a “bloc’s” votes are influenced by a single issue, the less easily can its votes be swayed. As the majority of American voters are not single-issue-oriented, the usual assumption is that their votes will be determined, if at all, more by party affiliation than by any other consideration. Those voters receive relatively little consideration in the sculpting of the parties’ and candidates’ platforms, as their loyalty is taken for granted.

     That leaves two “categories” of voters to trawl for electoral advantage:

  • The “independents,” registered to neither of the major parties;
  • The single-issue voting blocs.

     In the typical presidential contest, the independents don’t show a pronounced preference for either candidate. (There are exceptions, of course, as we saw in 1980 and 1984.) So the major parties tend to concentrate on the bloc voters...and those who “speak for” the bloc voters – i.e., those who issue endorsements in the name of some organization dedicated to the common interest – hold out for the very best deal they can get.

     Now, many would say that such organizations cannot command the votes of their members, and they would be absolutely correct in that. But they do exert influence, in some cases to the extent of being able to determine as much as 90% of the members’ votes. (This is often the case with occupation-oriented organizations.) If it were otherwise, the major parties would pay them no attention. So the parties do their damnedest to persuade the major figures in such organizations to endorse their candidates.

     This brings us to the ugliest aspect of the phenomenon: the corruptibility of organization luminaries.

     When representatives of a party or candidate approach the top figure in a special-interest organization, they are mindful of the potential cleavage between the organization’s nominal focus and the personal interests of the person they’ve approached. If such a cleavage can be found, it will be exploited. The “organization’s” endorsement makes it appear that the party or candidate has agreed to give high priority to the organization’s focus, but in truth it’s bribed the organization’s supremo to purchase that endorsement. Of course, the supremo won’t allow any hint of that to reach the membership, if he can help it.

     At last we come to the question of whether the votes of non-citizens might be important on November 8.

     There are several organizations that claim to represent the interests of illegal aliens. Those organizations possess considerable ability to sway illegals generally, as illegals tend to regard their immigration status as the most important thing about them. In other words, their cohesion as a bloc is greater than average. If they manage to cast votes two weeks from today, any influences on those votes will be of great importance – and the Democrat Party has all but openly trawled for those votes:

  • By impeding the identification, capture, and deportation of illegals;
  • By opposing the reinforcement of the southern border;
  • By opposing laws requiring voter identification;
  • By promoting “same day” voter registration;
  • By ridiculing the issue of vote fraud.

     Recent estimates hold that there are at least 12 million illegal aliens in the United States. If only a tenth of them manage to cast a vote on November 8, those 1.2 million votes, depending on their geographical distribution, could deliver 100 or more Electoral College votes to Hillary Clinton.

     So yes, it matters...especially since the true interests of anyone within the borders of this nation – whether legally or not – are physical and economic security, which can only be increased by greatly strengthened border control.

     Have you thought about volunteering to be a poll-watcher two weeks hence? It might be the most important spot of volunteer work you’ll ever do.


Cordolf said...

Not to quibble with your conclusion about the significance of illegal voting, which seems unassailable, but I'm just getting into the math.

The voter power calculation in your first example seems off to me. While the chairman gets his way 7/8ths of the time, isn't his fraction of decisive votes actually only 1/2? The other three voters then split the remaining half, for 1/6 each, don't they?

Here's my thinking:
Of the 16 cases, in three-quarters of them (12), the chair switching his vote changes the outcome.
In one-quarter (4) of the cases, voter 2 switching his vote changes the outcome.
Ditto for voter 3 and voter 4.

So of those 12+4+4+4=24 cases where a decisive vote is cast, half of them belong to the chair, and 1/6 each to each other voter.

Francis W. Porretto said...

Cordolf: The "standard" (i.e., the most common one, though there are others) definition of a voter's voting power is the fraction of configurations of the other votes cast in which his vote would decide the result. That's how I got my numbers.

Cordolf said...

Got it. As you note, I was working off of a different definition (the fraction of decisive votes that belong to a given voter among all votes cast in all cases - Banzhaf voter power calculation).

I'll have to dig in more - I always find this stuff especially interesting before a big election!

brinster said...

I'm going to draft a letter to my Congressman to initiate impeachment proceedings against madam pantsuit for high crimes and misdemeanors, if she gets elected. It's one of the few weapons we have.

Unknown said...

I don't understand the math, but I agree with your suppositions, and I would like to add that the importance of the freedom to communicate in all forms cannot be overemphasized. Hence, control of the internet now
is extremely pivotal, because of the general unawareness of those 'tween 18 and 38... they be good at using the phone, but poor on locating any specific country on the map, nor can they add up their grocery bill.
And I support brinster 100%... we can and should use the weapons we have always had to exercise the Constitution.