LINGUIST List 6.134

Tue 31 Jan 1995

Disc: Comparative Method

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1. , N-ary vs. Binary

Lloyd Anderson asks how n-ary (for n greater than 2) comparison
could EVER be worse than binary. Consider the problem of
heads and tails when we toss coins. What are the chances of
two coins (standing for two languages obviously) both coming
up the same (i.e., both heads or both tails) when tossed once?
Since there are four possible outcomes of the binary toss,
namely, HH, HT, TT, and TH, and only two where both come up
the same, the chances are 50%. But now consider what happens
when we toss three coins (standing for three languages). Since
a coin only has two sides, in each possible outcome at least two
of the coins come up the same. So the chances of 2 out of 3
coming up the same (which would correspond to saying let two out
of three languages agree in something and then they are related)
are 100% (which means this is not a valid test for relatedness).

Of course, if we had wanted all 3 out 3 to come up the same,
then the situation would be drastically different, but in
linguistics n-ary comparison never to my knowledge involves
such a requirement.

However, the only reason that n-ary comparison does so poorly
here is that (a) there are only two possible outcomes per language,
i.e., languages come in only two varieties, and (b) the number of
languages being compared is small (only three). The (a) part
is the one where real linguistic applications are drastically
different from our little coin-tossing game (since when you
look for language relationships, you are looking at hundreds
or thousands or maybe even more possibilities, not two, because
you are looking at phonological shapes of morphemes mostly, and
these allow lots of possibilities, at least thousands). So in
the real situations that alone insures that n-ary comparison is
better than binary. But it is also true that if you increase
the number of coins (languages) in (b), that also has the same
effect.

But you still have to be careful: the main concern is that given
n languages being compared you must worry about how many out of
the n are required to agree and about not making that number too
small (if you do, then again chance tends to take over).

Which raises a question: is there any published work on
comparing languages which explicitly calculates these numbers
(and does it right)?

Alexis MR