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Bitium
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March 29, 2013, 08:20:51 AM
 #21

While we are engaged in rhetorical gymnastics...

Given a Pareto type exponential distribution this is an estimate of how Bitcoin wealth distribution might shake out once all 21,000,000 BTC are generated. The table shows the population of each wealth group and the approximate BTC wealth that each member of that group would hold. It shows about half of all BTC wealth being controlled by some 4,000 individuals. 80% being controlled by only 1.5 billion people. With entry to "Middle Class", and even the "1%" being marked by an amount of BTC wealth that we would consider to be a transaction fee today. And the rest living on "dust".

1
7
31
155
771
3,843
19,203
96,003
480,003
2,400,003
12,000,003
60,000,003
300,000,003
1,500,000,003
5,500,000,003
923,589.76733184 BTC
32,985.34883328 BTC
9,310.38071907 BTC
2,327.59517977 BTC
584.91772514 BTC
146.68604153 BTC
36.69442650 BTC
9.17475329 BTC
2.29374566 BTC
0.57343928 BTC
0.14335996 BTC
0.03584000 BTC
0.00896000 BTC
0.00224000 BTC
0.00076364 BTC

I'm reading about Pareto Distribution now at http://en.wikipedia.org/wiki/Pareto_distribution

I'm curious, for the figures above, how did you choose xm and alpha?
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Rygon
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March 29, 2013, 05:44:38 PM
 #22

While we are engaged in rhetorical gymnastics...

Given a Pareto type exponential distribution this is an estimate of how Bitcoin wealth distribution might shake out once all 21,000,000 BTC are generated. The table shows the population of each wealth group and the approximate BTC wealth that each member of that group would hold. It shows about half of all BTC wealth being controlled by some 4,000 individuals. 80% being controlled by only 1.5 billion people. With entry to "Middle Class", and even the "1%" being marked by an amount of BTC wealth that we would consider to be a transaction fee today. And the rest living on "dust".

1
7
31
155
771
3,843
19,203
96,003
480,003
2,400,003
12,000,003
60,000,003
300,000,003
1,500,000,003
5,500,000,003
923,589.76733184 BTC
32,985.34883328 BTC
9,310.38071907 BTC
2,327.59517977 BTC
584.91772514 BTC
146.68604153 BTC
36.69442650 BTC
9.17475329 BTC
2.29374566 BTC
0.57343928 BTC
0.14335996 BTC
0.03584000 BTC
0.00896000 BTC
0.00224000 BTC
0.00076364 BTC

I'm reading about Pareto Distribution now at http://en.wikipedia.org/wiki/Pareto_distribution

I'm curious, for the figures above, how did you choose xm and alpha?

I just used the 80:20 rule, which would be an alpha of about 1.16. It's often used for doing off-the-cuff extrapolations like this.

http://en.wikipedia.org/wiki/Pareto_index

xm would just be unity, as in one indivisible person, which is probably not accurate because that sample is way out on the tail but it is fun to speculate what the richest person in the world would end up with. It is not quite as fun to see what the poorest person in the world would be left with, so the poorest 20% are lumped together in that sample. Exactly how divisible Bitcoin is would have little bearing on the nature of the distribution, which tends to hold up for global populations no matter what you do. You can also do it the other way, where xm is one satoshi. 

+1 to this analysis. I've seen two studies done with the distribution of coins across addresses, and it closely follows an 80/20 Pareto distribution. There was another good study a year or two back on some larger transactions that showed how someone with access to a very large amount of coins spread them out over several dozen smaller addresses. Sorry, I can’t find any of those articles right now.

I think it’s more realistic to calculate the distribution over 10 million people, since that’s a more realistic scenario anytime in the near future. For fun, I think about the total bitcoin balance as “experience” like in a game or something. As my BTC increases, I “level up” everytime it gets to be enough to fit into a higher tranch on the Pareto distribution. That’s roughly everytime the BTC balance increases by 4X.
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March 30, 2013, 02:01:41 AM
 #23

Funny thread.  No one bothered to notice that the math is off by a factor of 2.

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March 30, 2013, 03:07:01 AM
 #24

6.73 billion people / 21 million bitcoins == 322 people per Bitcoin  Wink

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March 30, 2013, 03:44:28 AM
Last edit: March 30, 2013, 04:00:30 AM by benjamindees
 #25

OP said "at this time".

Ah, I see.  I missed that.  Still, it's more complicated than that.  By buying Bitcoins, am I preventing others from having them, or am I helping to distribute them?  Would Bitcoins be more widely distributed at a low price, or at a high one?  If the Bitcoins don't already exist, then what are the miners "mining"?

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March 30, 2013, 05:48:54 AM
 #26

It is not the price that determines the distribution, but the distribution that determines the price.

In the long run.  In the short run, people want to use Bitcoin when the price goes up.

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March 30, 2013, 05:50:32 AM
 #27

It is not the price that determines the distribution, but the distribution that determines the price.

In the long run.  In the short run, people want to use Bitcoin when the price goes up.

I'm sure you could make this argument for the people who have them and want to spend them, but I'm not so sure about merchants.

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March 30, 2013, 06:39:07 AM
 #28

And now what if we imposed the Pareto rule on the Pareto rule itself: would the distribution be 64 of 80 and 4 of 20?

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Le Happy Merchant
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March 30, 2013, 07:50:22 AM
 #29

And now what if we imposed the Pareto rule on the Pareto rule itself: would the distribution be 64 of 80 and 4 of 20?

The top 20% of the top 20% have 80% of the top 20%'s Bitcoins, while the bottom 80% of the bottom 80% have only 20% of the bottom 80%'s Bitcoins.

Makes sense to me, I give it nine ten-out-of-tens out of ten.

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