David Cary asked ...

Does geometric consistency mean here that the candidates and voters
can be represented by points in some space so that a voter prefers
candidate A over Candidate B iff the voter is "closer" to A than to
B?

Basically, yes, any metric on the candidates would do, though the triangle 
inequality is not needed.
 
If you have four candidates, there are six pairs, so six distances.  Think of 
them as weighted edges in a complete graph on four vertices.  However, the 
actual lengths of the edges are not important, only their order. If  weight(AB) 
< weight(AC) ,   then consistency requires that A ranks B ahead of C.
 
Forest

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