put one's name in the hat

Etymology
From the informal practice of putting ballots into a hat, and then drawing a single ballot from the hat at random to decide the winner. When one put one's own name on a ballot in the hat, one would therefore be eligible to win.

Verb

 * 1)  To run in an election or to nominate oneself for consideration in some other selection process; to nominate someone other than oneself for such consideration.

Usage notes

 * Usually used to refer to a situation in which one nominates oneself, but sometimes used to refer to nominations of one person by others (as in the 1996 quotation above).