In politics sometimes it seems more important to not get the candidate that the majority of voters don’t want rather than the one that gets the most votes. Disapproval voting, i.e. putting candidates in order of disapproval, does not seem to be a good idea.
However rejection of the least wanted is a feature of AV. If one candidate is bottom of the list of by a sufficient number of the voters they cannot get in, however this only works if most of the voters rate all the candidates. This is very unlikely to happen particularly if there are lots of candidates. I think there are places where it was rating them was mandatory, but that’s a tall order if the party list includes The Judean People’s Front, the People’s Front Of Judea etc.!
My idea is for a format for the ballot paper in which instead of a column of boxes to be numbered that has to be numbered the is a square array of boxes with a row of boxes for each candidate which are ticked in order of approval going from left to right. To work only one tick is allowed in any row or column.
This has the immediate advantage that numeracy and legibility of the voters is no longer an issue.
The new thing is that voters can put tic as many candidates as they like where they like, so they could put just one tic for the one candidate that they really like or just one for the candidate really hate. Counting would be basically the same as AV, but I’ve not worked out the exact details.