[thaumasiotes]

> It is intuitively obvious that requiring probabilities to sum to 1 is rather arbitrary (any other number would seem to do as well)

Well, you have basically two choices -- one and zero. Any nonzero real number is trivially equivalent to 1.

It's not obvious to me, though, that 0 would work just as well?

[TeMPOraL]

Not only 0 and 1 are Schelling points - default options you can assume pretty much everyone would chose - they're also special in the way that they define a (positive) range where numbers always stay inside that range under multiplication. Two numbers between 0 and 1 multiplied together will always give a number that's also between 0 and 1. That's why a lot of places in math like to transform domains into the 0...1 range.

[closed]

This. Another way to express it is that for an interval [a, b], multiplying two numbers c, d within that interval will be within [aa, bb], and for 3 numbers [aaa, bbb], but it's super convenient to that for a=0 and b=1 these are always [0,1]. Other numbers would work, but would become cumbersome.

[thaumasiotes]

> for an interval [a, b], multiplying two numbers c, d within that interval will be within [aa, bb]

This only works when a is nonnegative. For example, the range of [-1, 1] under self-multiplication is [-1, 1], not [1, 1].

[MrQuincle]

Sum to 0 if probabilities are nonnegative scalars seem to be cumbersome. If probabilities are mathematical entities that are free to choose, the sum to 0 "can be played" by quite a few abelian groups.

I think it's especially important to be able to make a distinction between truth and falsehood however. If they are both 0, this is difficult. :-)