Dear Markus-- I'm sorry--I must have missed the part or P&P's Regularity definition that mentioned linear orders.
What they said was "PREFERENCES". I CAN'T GET RID OF THE CAPITALS, BUT WILL CONTINUE YOU SAID THAT THEY MEAN VOTED PREFERNCES AND THEN WHEN BLAKE SAID THEY MEAN ABSTRACT ORDERINGS YOU SAID THAT" WHAT THEY MEAN THEY SAID "PREFERENCES", AND DIDN'T QUALIIFY IT WITH SUCH WORDS AS "LINEAR'. I DON'T KNOW WHAT A LINEAR ORDIERING IS, UNLESS BY THAT YOU MEAN A RANKING. BUT REMEMBER THAT I REMINDED YOU THAT SINCE THE PREFERENCES ON THE BALLOT ARE THE INPUT TO THE COUNT, THEN BALLOT PREFERENCES ARE WHAT WE'RE TALKING ABOUT. THE PLURALITY BALLOT HAS VOTED PREFERENCES. I'M GOING TO CAREFULLY EXPLANI THAT TO YOU: SAY YOU VOTE FOR GORE. BECAUSE YOU VOTED FOR GORE AND NOT FOR BUSH, YOUR BALLOT SHOWS A CANDIDATE ORDERING FOR GORE OVER BUSH. YOU'RE VERY LIBERAL, AND FAST & LOOSE WITH YOUR INTERPRETATIONS OF WHAT PREFERENCE MEANS. THE DEFINITION DIDN'TSAY THAT A VOTER OR A BALOT had to show a full set of preferences. It only said the profile of indvidual preferences. You said that refers to the ones that are the input to the choice rule, and that means , for elections, the voted candidate orderings. All of them, in a Plurality election, consists of all of the voted preferences on the ballots. Tha't's unless you want to assume more unstated meanings. But as I said, none of this is relevant to the matter of whether your IIAC is Regularity. IT ISN"T <COMMA> BECAUSE YOU DON"T MENTION THE PROFILEOF INDIVIDUAL PREFERENCES<COMMA> AND SO YOUR IIAC HAS NOTHING IN ITS PREMISE THAT SAYS I CANT WRITE AN EXAMPLE THAT HAS DIFFERENT CAndidate orderings before & after thenew candidate is added. You still don't understand that, do you. But maybe you pride, and honor can be mistaken for a failure to understand a very simple and obvious differnce between your IIAC andREgularity. _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com
