# IID Vs Exchangeability

It is shown in Vovk (1986), in the binomial case, that the IID deficiency of a data sequence `⚠ $x$`

can be split into two components:

- the exchangeability deficiency of
`⚠ $x$`

- the randomness deficiency of the multiset of the observations in
`⚠ $x$`

(i.e.,`⚠ $x$`

with the order of its elements erased).

The problem is to extend this to general observation spaces.

Can we characterize, in a simple way, the randomness deficiency of a multiset (as in the second component above)? (In the binary case, this is done in Vovk 1986.)

**Bibliography**

- Vladimir Vovk (1986). On the concept of Bernoulli property. ''Russian Mathematical Surveys]], 41:247–248.