Democratic Currency

One project which implements something like this is 'Circles'. I remember it was on hold several years ago but seems to be running now - link

Your proposal is equivalent to a basic income funded by printing money. Where would this money derive its intrinsic value from?

Old commodity currencies were backed by gold or silver. Modern fiat currencies derive their intrinsic value from a tax system. (For example, a the US government demands taxes in dollars.)

To pay the every person a meaningful basic income, the average person has to lose that amount of value due to inflation by holding the currency and letting it be inflated away.

Who would want to be the person to hold this currency and lose massive value? For a new currency, it's especially problematic that the costs likely will go to the power users of the currency while lurkers get value for free which heavily desincentivies becoming a power user.  

Modern governments raise most of their revenue by raising taxes and not by printing money. A huge reason for that is the danger of hyperinflation. If you want to restribute money you can do that via raised tax money and pay an UBI, you haven't made a case why raising money via printing money is better then taxes. 

An important feature of governments is that they have the ability to uniquely identify their citizens and thus can give out benefits that go to every citizen equally. For an UBI ability to uniquely identify citizens is important to prevent citizens from signing up multiple accounts and getting more money.  

These days, when people try to think about alternative currencies, they often automatically think about cryptocurrencies. But before that, other ideas were invented and tried; some of them similar to what you want.

I am pretty sure the idea of automatically decaying currency is there somewhere. Actually, the governments would probably make something like that mandatory, to discourage people from using the alternative currency too much, and protect the position of the official money as something that (allegedly) decays more slowly. Because governments typically want to keep the monopoly on currency, but some of them are willing to allow alternatives, as long as those are somehow "crippled". (Technically, food stamps are already an "alternative currency".)  

Is starting capital really a bottleneck for entrepreneurs? Don't you just get money from investors? 
Elon Musk and Bill Gates only needed a laptop to start their business. Or, from Warren Buffet's biography: "In 1945, as a high school sophomore, Buffett and a friend spent $25 to purchase a used pinball machine, which they placed in the local barber shop. Within months, they owned several machines in three different barber shops across Omaha. They sold the business later in the year for $1,200 to a war veteran. ... In high school, he invested in a business owned by his father and bought a 40-acre farm worked by a tenant farmer. He bought the land when he was 14 years old with $1,200 of his savings. By the time he finished college, Buffett had accumulated $9,800 in savings".

The options between inflationary and non-inflationary options would be that a central authority print +25% new money and gives it away to eveyrone equally or that the central authority takes 20% of everybodys money and deals it out equally to everybody. This seems very similar to a flat tax arrangement. A lot of countries have even more aggreessively progressive taxation ie rich people cash in at more than 20% and poor people can end up getting more than the average. I don't know whether it being targeted to total wealth or at income is significant.

One could think of the arrangement also that everybody gets 1 stock of the "country" and then dividends are paid out per stock. Probably the main difference would be that stock are free to be transfered in deals while "citizenship stocks" would be inalienable. Otherwise some person migth end up holding multiple stocks like 3 (or say 2/3rds more for a total of 5/3 what everybody else has). Even if it would cost any finite amount of "current market power" "in the long run" it would be worth it.

I think the existence of centralised actor that is more clearly motived by public rather than private concern makes oriinary arrangements work. If all the actors have only private concerns it is unclear tome why I would want anybody else to have money. That is a alpha 0 money needs to be politically unfeasible in order for rich people to succum to any higher alpha. If part of the public concern is establishing and maintaining private property rigths then the tradeoff of paying the upkeep of maintaining the system makes sense.

I think this is equivalent to a UBI, where the amount of the UBI is pegged to the amount of money in circulation. You have certainly identified my big issue with capitalism - that it measures value by what the already rich value. And I think I like this way of scaling a UBI better than just a fixed dollar amount or even pegging it to the value of a fixed basket of goods (inflation). This would actually address long-term wealth inequality, and provide some incentive for the rich to spend down their wealth.

Edited to remove some kind of unintentional formatting issue with using dollar signs

One wonders how exchange rates would work with "traditional" currencies? There is little incentive to buy Democratic Dollars ('DDs' for short) with US dollars (just 'dollars', hereafter), for example, since the dollar is more durable over time. But buying dollars with DDs is probably a very good move. This imbalance should make the latter transaction all but prohibitively expensive. But if the exchange rates are uncoupled from buying power like that, one could simply spend their monthly allowance on (e.g.) gold and sell it later for dollars. Would we have to disallow direct exchange between the two systems? If so, what consequence proceeds from doing the gold thing anyway in order to hoard value derived from the DDs?

Perhaps the DD would only have buying power in certain sectors? I don't really see how that would prevent the exploit, though. It would only make it more complex.

I'm sure I would expect (e.g.) supermarkets to accept DD, but their profit margins are razor thin as it is. Having a percentage of that money decay every interval would be actively destructive to many companies unless there was a way to lock in value somehow.

I admit I haven't given it a huge amount of thought at this point, but I can't yet see how this system as presented wouldn't become something like a token that could maybe be used to place small bets between private parties, but which had no value in the goods economy.

The idea is intriguing, though. I'd be very interested for my first impression to be wrong on this one!