2005, Alan R. Andreasen, Social marketing in the 21st century, ISBN 1412916348, 9781412916349, page 50:
The ideal solution is to find individuals or agencies without what is often called "a dog in the hunt." Governmental monitoring organizations...and the World Health Organization (WHO), are probably the most reliable sources of raw data [for this issue]
This is often used erroneously to indicate that one has no stake in the outcome. As such this is a bastardization of two Southern idioms: "no dog in the fight," and "that dog won't hunt.” (The latter indicates something is a bad idea or prone to fail.) Use of the phrase "no dog in the hunt" when one wishes to indicate they have no "dog in the fight" will generate funny glances from any Southerners who overhear it.