# [EM] cyclic individual preferences

Alex Small alex_small2002 at yahoo.com
Mon Sep 6 16:53:04 PDT 2004

```A few more thoughts on the matter:

I've heard some plausible arguments for why a person might prefer A to B when those are the only 2 choices, and prefer B to C when those are the only 2 choices, but prefer C to A when those are the only 2 choices.

Fine.  Some might think it's irrational, others might think it's perfectly rational.  But those contexts of binary choices are irrelevant to an election with 3 or more candidates.

In an election with 3 or more candidates the context is quite simple:  We have to elect one candidate from a field of 3 or more candidates.  Whom will we elect?

You can hem and haw and deliberate all you want, but at the end of the day, after all of the cyclic psychological dilemmas and taxpayer-funded infomercials (um, I mean, party conventions), you have to pick somebody.  Whom do you want from amongst those candidates?

As soon as you answer that question you have broken your own internal cycle.  However rational and non-contradictory that internal cycle might (allegedly) be, the election is being held to answer the question "Whom shall we elect?"  And if we use a ranked method we have to follow it up with another question:  If it won't be the person whom you just named, whom else would you want elected?  As soon as you answer that question, you've just broken any cycle you might have had amongst the remaining candidates.  (Well, at least amongst some of the remaining candidates.  There might be 3 or more candidate remaining even after you indicate a second choice, so maybe there's a cycle amongst them.  The point is that you've at least reduced the number of candidates in that cycle, and declared that there are 2 candidates whom you prefer to all of the remaining candidates.  Anyway, that doesn't detract from the basic point.)

Anyway, I will grant this much:  If a method is only going to demand pairwise information then I have no objection to letting people vote cyclically.  It's no skin off my back if some people go in and indicate a cyclic preference on a ballot that basically asks them to fill in their own personal pairwise matrix.  But if the method asks for an ordinal preference relation, it would seem to me that letting them indicate a cyclic preference would greatly complicate matters.  Instead of inputting a simple list they'd have to be able to input substantially more information, complicating ballot design.

So, if a method can deal with cyclic preferences (e.g. a Condorcet method that only uses the pairwise matrix) and if the interface is compatible with cyclic preferences then I really don't care if people enter cyclic preferences.  However, I would never go out of my way to design a method to accomodate people who couldn't make a choice and break their cycles.

Alex

P.S.  Is it just me or did both conventions resemble informercials?  I kept waiting for Ron Popeil to spray some hair on Dick Cheney's bald spot, or give Bill Clinton a rotisserie oven so he can have a more heart-healthy diet.  And when the candidates unveiled their lists of impossible promises I was expecting one of them to say "But wait, there's more!  Vote now and you'll get ABSOLUTELY FREE a Swiss Army Knife that can cut through lead pipes!"  Anyway, I'll take that knife over a broken promise any day of the week.

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