'balloter' was formed in English from the noun 'ballot' plus the agent/verb-forming suffix '-er'; 'ballot' referred to a 'small ball' used for voting and '-er' denotes 'one who' or 'one who acts'.

'ballot' itself originates from Old French 'ballotte' (diminutive of 'balle' meaning 'ball'), used to denote the little ball used in voting; English adopted 'ballot' (Middle English) and later formed 'balloter' to mean one who ballots or to ballot.

Originally associated with the literal 'little ball' used in voting, the sense shifted to the act of voting or to someone who votes; 'balloter' came to mean 'one who votes by ballot' or 'to submit to a ballot'.