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<H2>Different Selection Rules</H2>
<H3><u>Blind Pick (BP)</u></H3>
<H4><I>easiest and simplest; can be used as lower bound on alignment
probability</I></H4>
<H3><u>Horse Race (HR)</u></H3>
<H4><I>requires evaluating N samples</I></H4>
<H3><u>Pairwise Tournament Elimination (TE)</u></H3>
<H3><u>Round Robin play (RR)</u></H3>
<H4><I>least efficient; but highest alignment</I></H4>
<H3><u>Other heuristics or knowledge-based rules</u></H3>
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<P>
It is also appropriate at this point to discuss the role of the selection
rules for picking the selected subset, S. So far we have only discussed two
such rules.
<P>
The first was Blind Pick (BP) which has the advantage of simplicity.
Nothing needs to be known about the problem. While BP is certainly not very
good, it is surprisingly robust and can often serve as a lower bound. The
second rule we have discussed is the Horse Race (HR) strategy. We evaluate
<i>N</i> sample performances using a surrogate or simplified model however
approximately. The universal alignment probability curves we calculated and
showed before can be used effectively to narrow down the search.
<P>
But many other selection rules are possible. Suppose one wishes to know the
best 16 tennis players in the world. One way to select them is to see who
reaches the quarter final in the U.S. Open tournament. Those who reach the
quarter final may not always be the top 16 seeded players but we know a strong
correlation exists. Historically, the quarter final players always include a
good sampling of the top-16 seeded players. In principle, we can calculate
the alignment probabilities in this case just as we have done for the HR
method. We intuitively know and can prove that such a tournament selection
rule is less computationally intensive than the HR rule but will yield a lower
alignment probability.
<P>
Similarly, the Round Robin (RR) method used in divisional championship play
for baseball teams is another selection rule. Intuitively, we know it will
have high alignment probability but requires more computation. The tournament
literature discuss many of these issues.
<P>
Finally, other selection rules based on heuristics and other knowledge can be
used. All are awaiting analysis.<BR>
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