The system ate my original post. This is a repost.
You may enjoy Urbano's unique analysis of political systems.
Urbano: "I wasn't even thinking of bribery as the mechanism. Partisanship or idealogical commitment would be enough of a driver.
Say you have a group of 100 people all committed to (for argument's sake) an ultra right agenda and conversely a list of people that they know disagree with them and they would not at all want to see in any elective position.
You would task them with just two directives: get themselves selected in a triad -or, if they find themselves in a triad with a person in their "hit" list, they would simply vote against that person.
Say person A is one of the 100 and he encounters person B -one of the persons on the hit list and person C in a triad.
If person A cannot persuade person C to vote for him, then he must simply vote against person B. Since he can't vote for himself, and neither can B, C holds the deciding vote, but A can force either a 3 way tie: A, B, C or a win for C if B votes for C. Either way, he has eliminated B from moving forward."
I think you have described a reasonable possibility. To some extent, the risk is attenuated among larger groups. In the New Jersey example I used to describe the process, there would be 1,879,126 groups at the initial level. The chances that one of the radicals is matched with one of the targets is quite small.
If the radical group were large, say one of the major unions, for example, they could pose a definite threat. However, to do so they would have to instruct a lot of people. That would reduce the possibility of their conducting their attack in secret.
As we traverse the continuum of possibilities from small secret cabals to broadly supported ideologies, we move from a highly diluted threat toward the ideal where the ideology or partisan group succeeds because it represents a broadly shared concept.
In a smaller sample, say in a community of 25,000 where a group of radicals are determined that someone not be allowed to become Mayor (for example), the possibility you describe is more likely.
Even then, though, the initial level will have over 8,000 groups. Some of the radicals might very well persist several levels so they can carry out their assignment ... but, by that time, they'd be opposed to whoever the other two candidates are by the nature of the system. They wouldn't be concentrating on expelling the target as much as they'd be concentrating on expelling both of the other members of their group so they can carry their agenda forward.
I think its also worthy of note that people with such radical commitments might very well alienate others who don't share their views. In that case, the possibility of their advancing far enough to carry out their task would be small.
Is it possible that a radical and a target will be assigned to the same group. Yes, but the odds are against that happening before the system has an opportunity to weed out the bad actors.
Urbano: "Would you consider starting with groups of 5 instead of 3? This would prevent a single person from hijacking the process."
Absolutely! There is nothing proprietary in any part of this concept. It's merely a starting place. Like the auctioneer says, "It doesn't matter where we start ... it's where we end up that counts."
I used a group size of 3 because it seemed like the easiest way to describe the concept. If group sizes of 5, or 7, or 9 offer more advantages than disadvantages. I'd be pleased with the change.
Some time back, when I was discussing this topic with my younger brother, Jim, I tossed out the notion of increasing the group size from 3 to 5, as you suggest. Here is his reply (I'll put my objection to one of his points at the end of his description.):
"Regarding expanding groups from 3 to 5, it seems that this might increase the probability of inconclusive results (or no winner).
With groups of 3, following the rules you specify there on only 2 possible outcomes:
2 votes for one member,
1 vote for another member of the group.
1 vote for each member of the group.
Your thesis is based on the assertion that the member receiving 2 of the 3 votes (the maximum allowed in groups of three) will be the more likely to provide leadership with integrity.
With groups of 5, assuming similar rules as in the case of groups of 3 (i.e. you must vote for one member of the group but cannot vote for yourself) 6 outcomes are possible (no one can receive 5 votes since no one can vote for themselves).
4 votes for one member, 1 vote for another member of the group.
3 votes for one member, 1 vote for each of two other members of the group.
3 votes for one member, 2 votes for one other member of the group.
2 votes for one member and 1 vote each for three other members of the group.
2 votes for one member, 2 votes for another member and 1 vote for a third member of the group.
1 vote for each member of the group.
In groups of 5 then, if only the candidate who receives 4 votes is considered likely to have adequate integrity to provide leadership, then the statistical probability of groups of 5 reaching a satisfactory conclusion (not deadlocked) will be quite a bit lower (1/6) than in the case of 3 member groups where the statistical probability will be 1 out of 2 possible outcomes.
This analysis is strictly mathematical and does not consider variables such as "human nature" or small group dynamics. Consideration of these variables will skew the distribution of results but is unlikely to render productive outcomes for groups of 5 more probable than for groups of 3."
My only objection to Jimmy's analysis is that I see no reason to stipulate that a candidate must receive 4 votes. A person who attracts 3 of the 5 votes will be fine. I don't even think it will be a problem in a particularly contentious group, where the "winner" only gets two votes.
On that basis, the top four of the six possible outcomes would produce winners. At first blush, groups of five seems like a more attractive alternative than groups of three. As you say, it lowers the possibility of one person preventing the selection of a "target" individual.
Urbano: "However, people form groups and groups form agendas.
In this section, you refer to the work of Robert Cialdini. I can't comment intelligently on that because I'm not familiar with his work. At the risk of putting my foot in my mouth, I think each individual will come into the triad with a clean slate as far as the group is concerned.
Effectively, they all start with a clean slate. If they have a commitment to a concept or ideal that predates the life of the triad, we can expect them to be loyal to that concept or idea ... but that's not a bad thing. As a matter of fact, that's the purpose of the process: It gives participants a chance to espouse their ideas as well as they're able. If they make their points with such force that they convince the two other people in their triad that they are worthy of representing them, they get a chance to try again at a higher level.
In and of itself, partisanship is not only inevitable, it is healthy. Our goal is to build a political system that responds to vested interests but is not controlled by them. The expression of ideas in the triads is a step in that direction.