Dr. Goldberg's board opponents, two of whom are Irish-American and two of whom are Hispanic, have also accused him of not hiring enough Irish or Hispanic supervisors.
The rationale was that the retirement of veterans would open slots for younger - and lower-paid - employees and also allow the board to hire more black and Hispanic supervisors.
The vote on Tuesday, and a possible runoff next month, are expected to produce the first Hispanic supervisor in 115 years in this heavily Hispanic county.
Money Will Be Scarce The election of a Hispanic supervisor could end a decade of conservative control of the county board.
There has been no Hispanic supervisor on the board since it was created 115 years ago.
Criteria for Redistricting A main question in drawing a district that would have the potential to elect a Hispanic supervisor was whether actual population data or just the numbers of voting-age citizens should be used.
Two Democrats with similar political views will compete Tuesday in an election that will produce Los Angeles County's first Hispanic supervisor in 115 years.
Last year, Maldef won a victory in Federal court against the gerrymandered supervisorial districts of Los Angeles County, where a Hispanic supervisor had never been elected.
Just last week, Los Angeles County elected its first Hispanic supervisor, Gloria Molina.
Only one, the St. Louis office, is directed by an Hispanic supervisor.