# IID Vs Exchangeability

It is shown in Vovk (1986), in the binomial case, that the IID deficiency of a data sequence can be split into two components:

- the exchangeability deficiency of
- the randomness deficiency of the multiset of the observations in (i.e., 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.