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PICK 20/50

On Wed, 25 Oct 1995, Gary Larson wrote:

> On Tue, 24 Oct 1995 Pacedebate@aol.com wrote:
> 
> > Thanks for your insightful comments. I will try to contact Rich Edwards. Do
> > you have any suggestions for change to the part that would be most difficult
> > to do. My intent was to maximize fairness. It isn't critical that it be done
> > this way and if necessary I will delete that line. 
> > Please change my Pick 50 proposal to a Pick 20 proposal by changing the line
> > that indicates the minimum number of judges who must be chosen from 50 to 20.
> > 
> > Thank you,
> > 
> > Tim Mahoney, Pace U.
> > 
> 
> I'm not sure that you want to go the route you are heading with the 
> revised proposal.  In the process of answering the criticisms concerning 
> how many judges should be selected (e.g. regional programs don't know 50 
> judges outside their region) you end up with a system that may have the 
> opposite of the intended effect.  On the surface, Pick 20 seems BETTER - 
> I only have to find 20 judges I like - but in the process I make it very 
> unlikely that I would ever receive any of them.
> 
> Given a pool of 150 judges (and ignoring regional constraints):  If we 
> assume "random behavior"  (most defenses of MP suggest - probably 
> incorrectly - that everone is preferred by someone and probably 
> sufficiently equally to insure that everyone judges their commitment)
> 
> Anyway the probability of a judge being picked is 20/150 = 2/15 = 1/7.5
> 
> The probability of a single judge being picked by both teams is 
> 20/150 * 20/150 = 400/22500 = 1 in 56.25
> 
> Since each team picks 20 judges the odds of at least one judge appearing 
> as picked by both teams is only 1 in 2.8.  Unfortunately, this 
> dramatically overestimates the computer's ability to place THAT judge in 
> THAT debate because of 1) regional constraints (the judges I pick may be 
> in my opponent's region), 2) the possibility that the judge that might 
> match has already heard one of the teams (if I am lucky in getting my 
> picks, by the fourth elim round I only have 9 judges left on my preferred 
> list rather than 20), and 3) the judge may already be assigned to another 
> round (unless I am in a break round and get first crack at the pool, the 
> odds of getting a match is extraordinarily low - of course this may be 
> your goal).
> 
> In any case given random behavior, pick 20 (of 150) will probably result 
> in less than 1 in 5 or 6 rounds getting a mutually preferred judge (1 in 
> 2.8 rounds in "best" case scenario if choices are random).  In fact, a 
> few teams scamming the system might conclude that it is best to pick all 
> the judges you really don't want to have because the odds of them being 
> mutually preferred by your opponent is VERY low and your choices would 
> further insure that they can't have any of the judges they want either.  
> "Rational" gambling might dictate this approach as appropriate.  Compared 
> to the present system, PICK 20 would likely decrease the number of 
> preferred judges that I get since the alternative to mutual picks is 
> MUTUAL non-picks.  If the rationale is that the purpose of the system is 
> to get fairness by insuring that my OPPONENTS don't get a preferred judge 
> this is a good model.  But I don't think that that is what you are after.
> 
> GARY
> 
> PS  Concerning your other question, I don't currently have an option 
> whereby you rank rounds by their breaking importance (e.g. round 6 -
> down 3, down 2, down 1, down 0, down 4, down 5).  That would not be 
> particularly difficult but it is new.  I would have much more difficulty 
> with the round two procedure of assigning judges first to rounds where 
> both teams didn't get preferred judges in round 1 ... (I have some ideas 
> but to accomplish this automatically would take some significant new 
> code).  Similarly, the elim process of assigning judges to the round with 
> the highest remaining seed is not at all straitforward (for my system).  
> I presume that if 64 beats 1, your proposal would require that the round 
> involving the 2nd seed would be panelled first rather than treating 64 as 
> if they were 1 or random as we do now.
> 
> AT this moment, I might feel obligated to publicly distance myself from 
> your proposal (something I have always been careful NOT to do as ES).  
> For that reason, you may want to suggest Rich's program as the 
> alternative - if he can do it (along with all of the other constraints of 
> our tournament).  I reckon that if push came to shove I would rewrite the 
> program to accommodate any or all decisions of the community but it would 
> cause some duress.
> 
> 
>
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