COUNTIFS Same array criteria PLEASE HELP

Hi there, I'm having trouble with a COUNTIFS function I'm trying to write. I'm checking the same criteria (an array) against multiple different ranges - is this possible? I can't figure out why else the function might not be working.

The file attached is a snippet of a much longer file. I'm trying to use functions to calculate the results of a single transferrable vote election. My problem is that the functioning doesn't seem to be counting beyond the second rank. So

Formula:

COUNTIFS($B$1:$B$20,$K4)

counts votes which selected the current candidate as their first choice. That works.

Formula:

SUM(COUNTIFS($B$1:$B$20,K$6#,$C$1:$C$20,$K4))

counts votes whose first choice has been eliminated and whose second choice is the current candidate. But the remainder - like

Formula:

SUM((COUNTIFS($B$1:$B$20,K$6#,$C$1:$C$20,K$6#,$D$1:$D$20,$K4)))

which should count votes whose first and second choices have been eliminated but whose third choice was the current candidate - are not counting.

I think you are right Ford, but if you are halfway through the process and there is more than 1 "valid value" a more complex formula is needed. However I feel the sample file doesn't contain enough information

If each column is a round of voting, we would need to know who is excluded at each stage and ideally why. Presumably you are keeping going until you have a winner.