In behavioral economics there exists the idea of the median voter theorem, but what does that mean?

Economists usually prefer the median when they want to describe data because the median can be more informative than the mean, especially when it comes to economic data.

In statistics, the mean is the average value of a set of numbers, while the median is the middle number of a set of data. The median is the number separating the lower half form the upper half of a set of data. In other words it is the middle number of a data set.

When we have a data set with 6 numbers: 2,2,3,4,5,10; then (3+4)/2 = 3.5 is the median.
If we have a data set with 7 numbers: 1,1,1,2,3,5,9; then 2 is the median.

For economical data, the median is oftentimes more informative than the mean because economic data is usually right-skewed which means it is biased against the mean value. Statisticians sometimes call the mean the least informative number because means usually do not tell you what you want to know, even if the data follows a perfect normal distribution (the ideal case for most statistical models). Economic data is almost always right-skewed so that the mean becomes more or less meaningless if one want to describe the state of the economy using means. In fact, the mean is very likely to misrepresent data.

For example, imagine a country with nine inhabitants that have a certain dollar amount to their name.

1,1,1,1,2,2,10,10 and 138 $ to be exact.

The mean for this data set is 18.4 $ but most people in this hypothetical country are very poor. The mean does not tell us that.

The median would describe the economic state of the country much more detailed because it is two. Most people in this country have little wealth and the median value reflects that.

Our hypothetical country is very poor and most of the wealth in the hands of one person. Two people are better off, while the rest is living in or near poverty.

This clear misrepresentation of the mean and median occur in politics also; where we call this the median voter theorem.

In politics, the median voter theorem postulates that a politician will always position himself so that he does not alienate left or right wing voters. Ergo, if the left is anti-military but pro-welfare and the right is pro-military but anti-welfare the politician will attempt to be neither pro nor anti-military as well as neither pro nor anti-welfare.

Politicians want to be in the middle of both extreme positions because having a pro-military stance would alienate all left leaning voters and lose the election. Likewise, taking a pro-welfare stance would alienate all right leaning voters and lose the election.

However, this is a huge problem because almost none of the voters will share these neither nor positions of politicians. In fact, most voters will either be pro or anti military and pro or anti welfare. None of them would be represented by a political agenda that aims to satisfy the median voter because most voters don't hold mediocre opinions about an issue.

When we apply this idea to our numerical example then the politics in our hypothetical country would be tailored to the 2s who are only 2/9th of the population. The 1s who are 4/9th of the population would not be represented, while the 10s and the 130 who make 3/9th of the population would also not be represented. In all likelihood, however, the 10s and 130 would not be interested in a change of the political system because they are fine with the status quo, while all other members of the hypothetical society would like want to see a change in the status quo.

For the same reasons; Plato wrote a whole book called the Republic which can be summarized as:
"Why democracy is garbage and should be abandoned", all though he chose better words to describe his idea and took the time to elaborate on why this is the case beyond a simple numerical example.

However, think about the huge step backwards that voting on Coinbase could actually mean for Crypto currencies.
Yes, voting is appealing to the masses but hypothetically; why give a bunch of people who have no interest in a given coin the power to vote against a coin? Coupled with the median voter theorem, any voting system that is designed is bound to select a coin that is most interesting to the median Coinbase user. And in the long run this would create the oppressive governmental system that would create a perpetual status quo which is - ironically - the main contributor to the emergence and creation of f Cryptos; the circumvention of governance of money by banks.

Granted; Coinbase members are probably informed and interested in Crypto currencies right now, but do all of them know everything about all coins? Do all of them want to learn about all coins? Do all of them have the time to inform themselves about all coins? These three questions show the crucial short-comings of an "official" voting system on Coinbase. It only has limited utility.

Just as it is in the political realm, most voters would be uninformed about what they are voting for or against.

For this reason Plato heavily criticized the Republic, while another critic Socrates was murdered by the government for his criticism.

In short, this voting for governance problem has existed for a very long time and has been discussed by many great thinkers over the epoches. All of whom reached similar conclusions; voting sucks.

Why should a Crypto voting system be any different?

For example, is it not conceivable that a SJW movement against "NAZI-coins" is used to benefit certain Crypto currencies over others? Where one group of voters is manipulated to vote against the emergence of new coins so that already established coins have an advantage over newcomer coins because these newcomers simply can't enter the system if they do not pass the vote? Of course this is a hyperbolic example but I hope you catch my drift.

Even if you think that this will never be a problem at all; there is no real reason to create a voting system on Coinbase.
Here is why:

Digital currencies can be easily implemented on any exchange. Their (mostly) open source codes are available on gitHub. This means that anyone who is capable of programming can check the code for errors and mistakes so that good coins can be selected by an open market. The best coins can be selected based on the open access code and passed onto exchanges. In addition, exchange members can petition and request the addition of certain coins to their exchanges or move to the exchanges that already list the coins that they are interested in. The process, is called the free market by economists and the free market already is a voting process in and of itself - there never is a need to create an additional layer of "official" voting. The problem with "official" voting is that it is oftentimes construed as a barrier of entry for the coins that could compete with already existing currencies. Of course, nothing speaks against community surveys that ask the community of an exchange if they are interested in certain coins or not, but in principle every coin that can meet the minimum requirements to be listed on an exchange should be able to get listed on that exchange regardless of an "official" voting-system for or against it.

If people are willing to buy and invest into the coin (and thus vote for the coin with their wallet) then the coin will be adopted. If the coins perceived added value is non-existent to the exchange it is well within the exchanges rights to reject listing that coin until some proportion of their members demand adoption or move away to an exchange where that coin is already listed. It is okay for exchanges to make decision on behalf of their members as long as they follow a set of rules that they apply to everyone.

In summary; voting for coins on Coinsbase is a terrible idea because Coinbase employees and coin-creators are capable of negotiating industry standards for coins without a broad voter base supporting or denying the adoption of certain coins over others. People who are experts and have experience working in the field are capable of evaluating new-coins that have value to their member base and can list them on their exchanges if they deem the coin to be a good fit. It is better for the exchanges to retain control over which coins they can list and which ones they cannot list. Of course, I am not suggesting the exchanges should not listen to their clients, in fact, I know that they will listen because if certain coins that are a good fit for their clients are listed somewhere else they will lose clients. Thus, they won't have an incentive to act against the interests of their clients.

For these reasons, I doubt that a public voting system would improve coin adoption; voting has been proven to be terrible time and time again over the course of history. If democracy is a perfect system then why did it succumb to the Roman empire? Let's not forget that most tyrants (Hitler & Lenin) for example, were voted into power. Voting is not the fail-save against bad governance. Centralization of power to people who are able to capitalize on the median voter theorem, however, is a good way to implement bad governance.