The Great Sanhedrin was too large (71 judges) to simply know how everyone voted. There must gave been a way to count votes, in a legal fashion. (Just counting people is prohibited.) So, by what mechanism did the Sanhedrin count votes?
See Sanhedrin 5:5 - Each participant is written down in 2 of three sets of scrolls - divrei hamezakin, divrei hamechayavin, and divrei hakol (this last one may only be a das yachid).
This documentation is important because in certain cases (mostly capital punishment), one cannot change his opinion from innocence to guilt.
When "voting," they start from either the end (for capital cases) or the middle/head of beis din (for other halachas) and voice their views. They only need to count the votes/opinions, not the people giving them.