If senator A votes with the party 80% of the time and senator B 70%, what is most and least that their votes can coincide?

70%

50%

A votes yes on 80 things out of 100.
B votes yes on 70 things out of 100.
30 of B’s no votes are on A’s yes votes.

90% and 50% respectively. The 50% is as @filmfann explained. The 90% is if B votes no to only 10% of A’s ‘yes’, and they agree on the rest.

90% and 50% sounds right. A and B together can agree with the party at most 70% of the time and they can together disagree with the party another 20% making 90% in all.

90% and 50% are correct.

The way I looked at it was to consider the times that the two senator disagreed with the party. We have 20% in the one case and 30% in the other. If there is no overlap in when they disagreed with the party, then the only time their votes coincide is when they both agree with the party, 100% – (20% + 30%) = 50%.

On the other hand, if the times when the 20% party disagreement is a subset of the 30% disagreement then the total agreement between the senators is the 20% overlap plus the 70% when they both agree with the party, 20% + 70% = 90%.

This is a convenient way of looking at it. The match in the votes of the senators grows with the overlap of the times they disagree with the party. For example, suppose the party is basically liberal and one senator is a social conservative and the other is a fiscal conservative. In this case the overlap in the dissent from the party will not overlap much and the two senators will not be that much in agreement, which is what we would intuitively expect.

Now that I think of it, the same kind of reasoning can be applied to the degree of overlap of agreements with the party.