"There are many reasons why the remain side lost the 2016 referendum, some contingent on the campaign itself and others stretching back decades."
(The Guardian.)
Does "contingent" mean "depend (depending?)" in the sentence above?
"Contingent" is a wrong word there.
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contingent on the campaigh seems fine to me.
Broadly speaking, it means 'happening to arise from the campaign itself'.
"...some contingent on the campaign itself and others stretching back decades." means: some of the reasons for the loss have their origin in the campaign itself, and others have their origin in things that happened decades before the campaign.