I see the flaw in Dash's math:


The attacker only needs less than 10 of the of masternodes which are eligible to authorize an InstantX lock for a specific UTXO. Because if InstantX requires all 10 masternodes to authorize (which I believe is what the white paper implies), then the attacker can block (i.e. jam) InstantX 65% of the time with only 1/10 of the masternodes! With 50% of the masternodes, the attacker could jam the InstantX 99.9% of the time. There is the 50% attack. This is probably why for Evolution, Evan changed the requirement to a simple majority (or some N-of-M) of each eligible quorum.

Dash's flawed math in the InstantX paper incorrectly assumes the attacker needs all 10 of the eligible masternodes.

Thus if the attacker owns 50% of the masternodes, the attacker has at least the 6/10th majority in 38% of the InstantX transactions and also can block (jam) the InstantX transactions 62% time with only at least a 5/10ths minority. Thus the attacker can attack 38 + 62 = 100% of the time. There is the 50% attack again. And Evan erroneously claimed that Evolution eliminates the 50% attack.  

That is the hypergeometric distribution.

https://en.wikipedia.org/wiki/Hypergeometric_distribution
http://math.stackexchange.com/questions/422414/probability-of-selecting-q-red-balls-from-m-red-balls-and-n-blue-balls

So enter here:

http://stattrek.com/online-calculator/hypergeometric.aspx
 

Population size:	1000 masternodes
Number of successes in population:	500 adversarial, colluding masternodes
Sample size:	10 eligible masternodes
Number of successes in sample (x):	6 needed for a majority