We also know a lot about what types of regimes are more susceptible to democratization. A democratization effort in Vietnam is much more likely to succeed because Vietnam is a party state, has some elections, has a strongish economy, etc. I can say more about that too.

First off, remove democracy from your lexicon. It's too complicated and confusing word, it means different things to different people. Usually if you bring democracy into this debate you get a circular answer by accidentally assuming many institutions at once.

A good starting question here is to think about the service recipients. What is the theory of change for how they compel the state to provide services under each system? What assumptions are needed for it to work?

Citizens have to coordinate to punish a leader that does not provide services if they want more services than the leader prefers to provide. So steps are:

1. Citizens must want services.
2. Citizens must find out if services are provided and if better provision is possible.
3. Citizens they must communicate to eachother both the information and their awareness.
4. Citizens they must coordinate to punish simultaneously because individually attack leaders is ineffective and punishable.
5. If they want to prevent leaders from counter punishing (repression), citizens must punish repression (see above steps).
6. Citizens must choose public goods over selling their votes.

Elections make the later steps easier by coordinating simultaneous punishments (election day). Experienced oppositions make 2 and 3 easier. If 1 or 6 are violated, you won't get any benefit though. Also if the middle class solves this and the poor do not, guess who gets service...

The short answer is that many countries democratize but see little benefit for public service because this is a really long chain that can break down easily.

I may come back and find the studies for this stuff.