> > I've got an algorithm for computing the probability of a candidate in
> > the presidential election winning a certain number of elector votes
> > that looks like this (in pseudo-code):

> >   define compute-ev-probabilites (state-probs)
> >     probs = make-array 0 .. 538
> >     probs[0] = 1
> >     foreach state-prob in state-probs
> >        fold-into probs state-prob.votes state-probs.probability

> >   define fold-into (probs votes prob)
> >     for i from 538 downto 0
> >       probs[i] = probs[i] * (1 - prob)
> >       if (votes <= i)
> >         probs[i] = probs[i] + (prob * probs[i - votes])

> > So far so good. Now I'd like to add this function which can back out
> > the effects of a single state:

> >   define back-out (probs votes prob)
> >      for i from 0 to 538
> >       if (= prob 1)
> >         probs[i] (i + votes) < probs.length ? probs[i + votes] : 0
> >       else
> >         if (votes <= i) probs[i] = probs[i] - probs[i - votes] * prob
> >         probs[i] = probs[i] / (1 - prob)

> > Mathematically this works--I've actually implemented this in Common
> > Lisp and when I use arbitrary-precision rational numbers it works
> > perfectly. But when I use floating point numbers the computations in
> > back-out get wildly out of whack. As best as I can tell this is
> > because small errors introduced because (x * y) / y isn't necessarily
> > exactly x get propagated throughout the whole array of probabilities
> > and perhaps amplified by inaccuracies in the subtraction. (I can't
> > just use rationals because I'm actually implementing this in
> > Javascript whose only numeric type is double float.)

> > Is there some obvious way to write this so I can still use floating
> > point numbers but have back-out work properly. I'd be happy to trade
> > some precision for reversibility.

> > -Peter

> If you are doing a lot of manipulations this numers that are 1 - eps
> it may pay to use a bit of symbolic smarts to keep the 1 separate from
> the eps. How to do this "depends". Working through an error analysis
> should tell you where it might help. You would be using the symbolic
> analysis to lower the sensitivity of the computation to error progation.

> However since you had to ask one suspects that you may not be familiar
> with doing the error analyses. (Yet another variation on the classic
> comment on the pricing of yachts!)