This researchpost is a compilation of a number of responses I have given over the years, extended with a lot of new content and references. Until Voat adds some way to nest content, appendices are in the comments. Enjoy.

I don't understand the logic of voaters who apparently want a lawless society, but very likely would not want to personally be victims of unlawful force or violence.

You've (likely unknowingly) baked a false dichotomy into your question. More specifically, your question presupposes either a police force, or nothing to ensure law at all.

First, what you probably think of as the 'police' actually comprises a number of distinct groups with differing origins, that each have slowly scope-creeped until they blended with each other. For example, cities have 'police' proper, counties have sheriffs, states have troopers, feds have marshals, the Secret Service came from the Treasury, the IRS/ATF/DEA/BLM all have their own militarized 'police forces', etc. All of these have blended together where nobody can tell them apart anymore (scope creep from earlier).

Sheriffs are elected, and have always been so, and, as a result, they are naturally accountable to the county that elects them. Sheriffs in larger counties would have deputies to assist them. This is they way it's always been. This is the only law enforcement that has existed from the beginning. This is the only law enforcement that is (or was, in the past) directly accountable to the people who pay for them. This is the only police needed for a lawful society, and that is harmonious with society. None of the other 'police forces' are harmonious with society, and in some (possibly all - still researching) cases, they are actually unconstitutional.

Unlike any other 'police force', a Sheriff's relation to his county had natural checks and balances. For example, since the force was naturally small, the sheriff would actually have to go door-to-door and roust able-bodied men to assist the sheriff in large operations. Large operations against civilians like gun grabs, forced evacuation (a la Katrina), WACO, or the Bundy ranch couldn't have existed as it would need the support of the people - the people are largely self policing.

It extends further - originally, the police's authority to arrest came from the citizen's constitutional authority to arrest (modern propaganda reverses this). The citizen had full authority - a citizen could arrest a man, walk him down to the sheriffs office, and charge him with a crime. This is before 'the state' had their own lawyers (called district attorneys/prosecutors), and usurped a monopoly on justice (the 'how' is too long of a story for here). This is also where a lot of the corruption first snuck in.

The disarming of the people is nearly complete. Although not specifically forbidden, the mechanisms that allow a citizen to criminally charge another (bypassing the state entirely) are vestigal at this point (but not nonexistant - there are a few tests in the wild at the moment). Most of 'the state' cannot be charged anymore with anything (in any case, they won't charge themselves). Citizens' arrest rules vary widely and, even though on paper they are more lenient than for arrests made by law enforcement (regarding probable cause, anyway), police forces can never be held civilly or criminally liable for a wrongful arrest, excessive use of force, or for tort damages arising from the same. This is how they can make wrongful arrests without penalty, use excessive force without penalty, and, in extreme cases, kill the wrong people with no recourse at all (there are a ton of these - just search 'police shoot wrong house'/'police kill wrong man'/etc - nobody is ever accountable).