The reason for the split in New Jersey's electoral vote in 1860 is this:
At the time one voted for the individual electors by casting a ticket with the names of the various electors printed on it. If one did not want to vote for a particular elector then one could cross out their name and a vote would not be counted for that individual.
The opposition to Abraham Lincoln combined into a fusion ticket of 3 Douglas electors, 2 Breckenridge electors, and 2 Bell electors. When election day came around, the vote total difference between the two tickets (pro-Lincoln, and anti-Lincoln) was pretty close. The Anti-Lincoln ticket did indeed get the most votes, but enough people casting that ticket crossed off the names of the 4 Bell and Breckenridge electors that they got less votes than the Lincoln electors electing the 4 with the highest vote total. I assume that this was done by people who had a pro-Northern sentiment who had no problem voting for Douglas, but didn't want to vote for electors for what were perceived as pro-south/pro-slavery candidates.
In addition, in New Jersey, the Breckinridge and Bell electors were not the same in all counties.
This was prior to the adoption of the Australian ballot in the United States, and elections were actually all write-in. However, political parties could print up ballots with lists of their favored candidates. Voters could edit these ballots, because they were in fact casting a write-in ballot. Or they could simply write their only list.
The conventional practice in cases where electors were chosen as individuals is to report the vote total of the leading candidate of each slate.
