Sixteen Bit Voting

Some voting machines in Broward County can only count 32,000 votes per precinct. Translating this to tech terms, it could probably count up to 32,767 votes, which is a bit of a magic computer number. It's the largest number a 16-bit signed integer can hold. Why, oh why, is this an issue in this day and age? Are those extra two bytes so precious? 536,870,912 bytes cost only $95.99. I'm sure we could afford to spare a couple.