When I was growing up in a small,a very small, village back in the 1940s and 50s the peace of the community was often shattered by a massive dogfight in the "Main" street. Dogs, in those days, were allowed to wander at large through the parish and a fight was a natural occurrence when any "outsider" dog ventured into unfamiliar territory. This often happened at night.
If the fight continued unabated for 10 minutes or more, the local policeman would begin knocking on doors and enquiring "Have ye a dog in this fight upstreet ?"
If not, one had no further business in becoming involved and thus gave rise to the saying "I've no dog in this fight !".

An' that's no lie.