Replanting saved shallots?

I'm very familiar with planting garlic cloves from the harvest earlier in the year. In my experience if you plant the large plump cloves then you are rewarded the following year with fat bulbs.

Can you do the same with shallots? If so does the same principle work on size? 

I should mention that I don't appear to have any onion white rot on the plot.

Small shallots produce large shallots but less of them big shallots produce lots of small shallots.
So I'm told. Reasonably accurate this year compared to last year where I did it the other way round.