I think I explained that in detail before.  
In a "repeated vote" system, you base the others' behavior on their strategy in the "previous" round (that's all you know) and you optimize the outcome for yourself by picking your own optimal strategy GIVEN the strategy of the others. 

If the strategies taken by everybody in the previous game is a Nash equilibrium, then everybody will take the SAME strategy again in the next round.  So everybody's strategy will remain stable throughout successive rounds.