Every political system that's ever been tried has proved to be open to abuse.
There is "open to abuse."
And there is "chisel the locks off the doors, prop them open with giant lead weights, and send a gilded invitation by special courier to abuse's house saying "COME ON AND ABUSE THIS, YOU ABUSIVE ABUSER YOU, COME ON, DO IT, YOU KNOW YOU WANT TO!"
Systems with artificially limited franchise where you have to go through some kind of "federal service" to become a voting citizen are very much the latter.
And in this system the abuse is not who get's to take part or not as the laws would specifically prevent that. Rather as the individual would have little choice as to what role they have to fill, who gets the most dangerous jobs with the highest risks to life and limb and who gets to sit in a nice warm office organizing things or working in social programs in holiday resorts.
Group A gets to drain salt marshes in the middle of winter. Group B looks after the elderly in one of God's Waiting rooms by the sea. Group C gets to serve as assistants to members of the Government (Who by some strange quirk of fate happen to be good friends of their Grandparents)
That's just the start of it. There's also the question of who gets dishonorably drummed out of the service (and thus is made permanently ineligible to vote), and why.
Sexual or gender presentation that doesn't line up with what the service thinks you should be? Moral turpitude. Dishonorable discharge.
Signs of political radicalism or discontent, during or prior to term of service? Moral turpitude, insubordination, prejudicial to discipline. Dishonorable discharge.
Membership in a disliked minority group? Systematically given the stink-eye by all the senior officers, who will assuredly drum you out of the service unless you constantly struggle to prove you are one of "the good ones."
Quite bluntly, while I disagree with people who call Heinlein fascist, it is the plain and simple truth that a system like Heinlein's Terran Federation is one of the most efficient ways I can imagine to implement fascism while keeping up the pretense of being a republic.
After Athens embraced Democracy, well created it, post Persian war, did not all citizens have to take turns participating in civil service?
That wasn't Athens' qualification for citizenship, though. Their qualification for citizenship was "be a male descended on both sides from other Athenian citizens with no foreign ancestors whatsoever, who is not a slave."
Now, certain things were
expected of able-bodied adult citizens, such as that when Athens went to war, you'd pick up a javelin (or a suit of armor if you could afford it, in which case you had more privileges) and go join the army. Or maybe if you were poor (and therefore
bad, this was a clear value judgment in a society that invented 'aristocracy' to mean 'rule by the best') you would accept a salary to be a rower in the Navy. But that wasn't something you did in order to be a citizen. It's just that your community tacitly expected you to come along for things like this, and the pressure was far too high for most people to turn down.
The thing is, modern societies do not actually require the semi-coerced labor of every able-bodied and motivated individual working "in the service of the state" for free or for subpar wages. It's not really necessary. Modern economies do not run on corvee labor, and there is no need to come up with some fancy workaround for corvee labor or conscription in which people are forced to submit to such labor or be second-class citizens for life.
Just have the government tax the citizenry and pay people to do government jobs, like a normal country. All this obsession with "we need the vote to only go to people who appreciate it properly" is either a sincere attempt to solve a fake problem that doesn't actually exist, or a real attempt to institute various forms of limited democracy, military rule, or caste system via the back door.
This is why I'm modifying the idea so that you don't have to serve in the military, but can also do so in some government run program that benefits the nation as a whole. Conservation, Forestry, Nation infrastructure construction and maintenance, social health care ect. The point being you earn the franchise by spending a period of time doing directed work that benefits the nation.
I think it's worthwhile here to try and be clear:
Are you asking "what would happen in a society that instituted System X" or are you trying to subtly say "System X is super-cool and I'm sure I can fix any minor problems with it and then clearly it will be superior to what we have now?"
Limiting it to those willing to earn it, and having had earn it be less likely to take it for granted.
Why is this a priority?
We know why Heinlein SAID it was a priority. But bluntly, he thought it was a priority because he thought that what America really needed in the late 1950s and early 1960s was to be more warlike and confrontational with the Soviets, more paranoid of possible communist infiltration on the home front, and more aggressive in disciplining Those Pesky Kids (that is, the late Silent Generation and early Baby Boomers) who were clearly a bunch of juvenile delinquents and needed a good (totally not fetishized) whipping to teach them some proper American values.
In short, Heinlein was very, very out of touch and was horribly wrong about what American society of the time needed at the time he wrote
Starship Troopers. It seems reasonably likely that an America he was genuinely happy with would have fucked around and found out to the extent of getting into nuclear war with the USSR.
These are very different things to try to accomplish with a thread, and it makes a difference in how I or others might engage with you.
You will note that even in the book the system is a result of a social upheaval that basically forced a group of veterans to risk themselves to creat a stable environment for their families and communities and as a result the decided that they would only let fellow vets have a say in how things were ran. And this system spread.
More precisely, this is the propaganda version spread by the world government after the "veterans' societies" in question
became the world government.
I see no reason to imagine that the veterans' associations that became the Terran Federation in
Starship Troopers were morally or politically all that different from the far-right militant Freikorps of Weimar Germany. Whether those groups were "forced" to do everything they did, and to adopt all the policies they did, and to shape politics as they did, would depend heavily on whether one is more inclined to agree with Hitler, or with the sort of people he liked to throw in prison camps for political dissidence.
It does have one potential advantage to a government. Those willingly risk there lives can do so to become part of the government instead of overthrowing said government. Thus tending to limit the likelihood. of armed rebellion,
I'm not sure that actually works, as opposed to being the kind of self-congratulatory "and this is why our system is best" stuff that any class focused on feeding 'correct' political and ideological propaganda to high school students would do a lot of.
The clear implication of the argument Heinlein gives us, and that you relay to us, is that there is a 1:1 correlation between "willingness to take risks," "moral virtue," "civic-mindedness," and "agreement with the clearly good, proper, and mathematically correct moral values of the Terran Federation." In actual practice, these things are not tightly correlated. Mahatma Ghandi would score very high on the first axis, debatably high on the second, very low on the fourth, and whether he would score high or low on the third depends entirely on whether you grade him as a person who's supposed to be a loyal British subject or an independent leader of the nation of India.
The question is whether such systems will encourage people to vote. Will we say "I've earned my 5 votes and I'm damn well going to use them" or will others say "What's the point of my single vote, those 5-voters have all the power?"
Both. If you are a first-class citizen (that is, if you are some combination of educated, a wealthy businessman, high-status in your community, and the over-45 parent of two) you will be very sure to vote.
If you are a second-class citizen, you will not see much point in voting; the system will by design make your opinion irrelevant. That is a feature, not a bug, from the point of view of the kind of person who implements this.
Also, expect a system like this to make whatever institutions gatekeep things that give access to more votes
very careful about the qualifications they hand out, and under a lot of external scrutiny. If getting a university degree means you get to vote twice, expect a lot of people questioning whether any given university should be accredited or not, mostly on ideological grounds.
Goodhart's law applies here:
"Any measure which becomes a target will then become a bad measure," because people start gaming the system. You'll see a huge business in multinational corporations who rotate citizens through overseas postings for two years just to be able to say they have done so, in universities that award whatever minimum degree grants you an extra vote via as many correspondence/virtual courses as possible, and so on.