Being intransigent and shaking heads, demonstrating partiality (4)
I believe the answer is:
bias
'partiality' is the definition.
(I know that bias is a type of partiality)
'being intransigent and shaking heads' is the wordplay.
'heads' suggests taking the first letters.
The initial letters of 'being intransigent and shaking' is 'BIAS'.
'demonstrating' acts as a link.
(Other definitions for bias that I've seen before include "could be binding" , "Prejudice, partiality" , "Unfairly influence" , "colour" , "Prejudiced or weighted opinion" .)