What do you mean by 'administer' elections? I imagine that they must be overseen at the precinct level and then aggregated up to the county level, before being aggregated at the state level. If there is a block at the county level with poor aggregation, it can certainly throw a wrench into things. Is it done differently in Texas?
In Texas, state elections are administered by the counties, typically by the county clerk; with the tax assessor-collector keeping the voting rolls (a vestige of when Texas did not have voter registration; and you would bring your poll tax receipt to vote). Some counties have independent election administrators who are appointed (the county clerk and tax assessor-collector are partisan elected offices).
Each county will prepare the ballots, buy/rent voting machines, define election precincts, arrange for polling places, hire election judges and clerks, maintain voting rolls, Each county would finance their own elections.
This is not to say that there aren't state standards and requirements that the counties must comply with, and that their isn't some state funding, but primary responsibility in on the county level.
On election night the votes are tabulated for each election precinct and each office at the county level. The vote totals for statewide and multi-county offices are transmitted to the state level where they are added together. If there is a recount each county would conduct the recount of the votes cast in the county.
Cities, school districts, MUDs and other districts are responsible for administering their own elections. Sometimes they contract with the county to conduct the election, and counties can conduct unified elections, so you might not only vote for state legislator, but school board member on the same ballot. In other instances, the city or school district may just rent the voting equipment and other services from the county, and have their own polling places, and in other cases they might simply do everything themselves with paper ballots. Cities and counties may extend across county lines, so a city or school district might have to coordinate with more than one county. In all these cases, the county would provide the voting rolls, since registration is maintained at the county level.
I won't try to explain party primaries.
I think this is a fairly standard administrative structure particularly in the South and West where there aren't townships, or townships have limited government functions. Alaska and Hawaii administer elections statewide. Alaska doesn't have anything like counties, at least not across the state, and Hawaii doesn't have significant county governments.
But areas in New England where there towns and townships are the main level of universal local government, and counties are only used to make the census bureau happy, may administer elections at the town level. Wisconsin and Michigan, which were strongly influenced by New England also administer election at the town level.
So it is my understanding is that whoever is responsible for Waukesha County elections is mainly responsible for totally votes from elections administered by townships in the county. Since the primary theme of the Democrats is victimization, they have to blame someone for anything and everything.
