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On Inflation, Transaction Fees and Cryptocurrency Monetary Policy

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Vitalik Buterin


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On Inflation, Transaction Fees and Cryptocurrency Monetary Policy

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The primary expense that must be paid by a blockchain is that of security. The blockchain must pay miners or validators to economically participate in its consensus protocol, whether proof of work or proof of stake, and this inevitably incurs some cost. There are two ways to pay for this cost: inflation and transaction fees. Currently, Bitcoin and Ethereum, the two leading proof-of-work blockchains, both use high levels of inflation to pay for security; the Bitcoin community presently intends to decrease the inflation over time and eventually switch to a transaction-fee-only model. NXT, one of the larger proof-of-stake blockchains, pays for security entirely with transaction fees, and in fact has negative net inflation because some on-chain features require destroying NXT; the current supply is 0.1% lower than the original 1 billion. The question is, how much “defense spending” is required for a blockchain to be secure, and given a particular amount of spending required, which is the best way to get it?

Absolute size of PoW / PoS Rewards

To provide some empirical data for the next section, let us consider bitcoin as an example. Over the past few years, bitcoin transaction revenues have been in the range of 15-75 BTC per day, or about 0.35 BTC per block (or 1.4% of current mining rewards), and this has remained true throughout large changes in the level of adoption.



It is not difficult to see why this may be the case: increases in BTC adoption will increase the total sum of USD-denominated fees (whether through transaction volume increases or average fee increases or a combination of both) but also decrease the amount of BTC in a given quantity of USD, so it is entirely reasonable that, absent exogenous block size crises, changes in adoption that do not come with changes to underlying market structure will simply leave the BTC-denominanted total transaction fee levels largely unchanged.

In 25 years, bitcoin mining rewards are going to almost disappear; hence, the 0.35 BTC per block will be the only source of revenue. At today’s prices, this works out to ~$35000 per day or $10 million per year. We can estimate the cost of buying up enough mining power to take over the network given these conditions in several ways.

First, we can look at the network hashpower and the cost of consumer miners. The network currently has 1471723 TH/s of hashpower, the best available miners cost $100 per 1 TH/s, so buying enough of these miners to overwhelm the existing network will cost ~$147 million USD. If we take away mining rewards, revenues will decrease by a factor of 36, so the mining ecosystem will in the long term decrease by a factor of 36, so the cost becomes $4.08m USD. Note that this is if you are buying new miners; if you are willing to buy existing miners, then you need to only buy half the network, knocking the cost of what Tim Swanson calls a “Maginot line” attack all the way down to ~$2.04m USD.

However, professional mining farms are likely able to obtain miners at substantially cheaper than consumer costs. We can look at the available information on Bitfury’s $100 million data center, which is expected to consume 100 MW of electricity. The farm will contain a combination of 28nm and 16nm chips; the 16nm chips “achieve energy efficiency of 0.06 joules per gigahash”. Since we care about determining the cost for a new attacker, we will assume that an attacker replicating Bitfury’s feat will use 16nm chips exclusively. 100 MW at 0.06 joules per gigahash (physics reminder: 1 joule per GH = 1 watt per GH/sec) is 1.67 billion GH/s, or 1.67M TH/s. Hence, Bitfury was able to do $60 per TH/s, a statistic that would give a $2.45m cost of attacking “from outside” and a $1.22m cost from buying existing miners.

Hence, we have $1.2-4m as an approximate estimate for a “Maginot line attack” against a fee-only network. Cheaper attacks (eg. “renting” hardware) may cost 10-100 times less. If the bitcoin ecosystem increases in size, then this value will of course increase, but then the size of transactions conducted over the network will also increase and so the incentive to attack will also increase. Is this level of security enough in order to secure the blockchain against attacks? It is hard to tell; it is my own opinion that the risk is very high that this is insufficient and so it is dangerous for a blockchain protocol to commit itself to this level of security with no way of increasing it (note that Ethereum’s current proof of work carries no fundamental improvements to Bitcoin’s in this regard; this is why I personally have not been willing to commit to an ether supply cap at this point).

In a proof of stake context, security is likely to be substantially higher. To see why, note that the ratio between the computed cost of taking over the bitcoin network, and the annual mining revenue ($932 million at current BTC price levels), is extremely low: the capital costs are only worth about two months of revenue. In a proof of stake context, the cost of deposits should be equal to the infinite future discounted sum of the returns; that is, assuming a risk-adjusted discount rate of, say, 5%, the capital costs are worth 20 years of revenue. Note that if ASIC miners consumed no electricity and lasted forever, the equilibrium in proof of work would be the same (with the exception that proof of work would still be more “wasteful” than proof of stake in an economic sense, and recovery from successful attacks would be harder); however, because electricity and especially hardware depreciation do make up the great bulk of the costs of ASIC mining, the large discrepancy exists. Hence, with proof of stake, we may see an attack cost of $20-100 million for a network the size of Bitcoin; hence it is more likely that the level of security will be enough, but still not certain.

The Ramsey Problem

Let us suppose that relying purely on current transaction fees is insufficient to secure the network. There are two ways to raise more revenue. One is to increase transaction fees by constraining supply to below efficient levels, and the other is to add inflation. How do we choose which one, or what proportions of both, to use?

Fortunately, there is an established rule in economics for solving the problem in a way that minimizes economic deadweight loss, known as Ramsey pricing. Ramsey’s original scenario was as follows. Suppose that there is a regulated monopoly that has the requirement to achieve a particular profit target (possibly to break even after paying fixed costs), and competitive pricing (ie. where the price of a good was set to equal the marginal cost of producing one more unit of the good) would not be sufficient to achieve that requirement. The Ramsey rule says that markup should be inversely proportional to demand elasticity, ie. if a 1% increase in price in good A causes a 2% reduction in demand, whereas a 1% increase in price in good B causes a 4% reduction in demand, then the socially optimal thing to do is to have the markup on good A be twice as high as the markup on good B (you may notice that this essentially decreases demand uniformly).

The reason why this kind of balanced approach is taken, rather than just putting the entire markup on the most inelastic part of the demand, is that the harm from charging prices above marginal cost goes up with the square of the markup. Suppose that a given item takes $20 to produce, and you charge $21. There are likely a few people who value the item at somewhere between $20 and $21 (we’ll say average of $20.5), and it is a tragic loss to society that these people will not be able to buy the item even though they would gain more from having it than the seller would lose from giving it up. However, the number of people is small and the net loss (average $0.5) is small. Now, suppose that you charge $30. There are now likely ten times more people with “reserve prices” between $20 and $30, and their average valuation is likely around $25; hence, there are ten times more people who suffer, and the average social loss from each one of them is now $5 instead of $0.5, and so the net social loss is 100x greater. Because of this superlinear growth, taking a little from everyone is less bad than taking a lot from one small group.



Notice how the “deadweight loss” section is a triangle. As you (hopefully) remember from math class, the area of a triangle is width * length / 2, so doubling the dimensions quadruples the area.

In Bitcoin’s case, right now we see that transaction fees are and consistently have been in the neighborhood of ~50 BTC per day, or ~18000 BTC per year, which is ~0.1% of the coin supply. We can estimate as a first approximation that, say, a 2x fee increase would reduce transaction load by 20%. In practice, it seems like bitcoin fees are up ~2x since a year ago and it seems plausible that transaction load is now ~20% stunted compared to what it would be without the fee increase (see this rough projection); these estimates are highly unscientific but they are a decent first approximation.

Now, suppose that 0.5% annual inflation would reduce interest in holding BTC by perhaps 10%, but we’ll conservatively say 25%. If at some point the Bitcoin community decides that it wants to increase security expenditures by ~200,000 BTC per year, then under those estimates, and assuming that current txfees are optimal before taking into account security expenditure considerations, the optimum would be to push up fees by 2.96x and introduce 0.784% annual inflation. Other estimates of these measures would give other results, but in any case the optimal level of both the fee increase and the inflation would be nonzero. I use Bitcoin as an example because it is the one case where we can actually try to observe the effects of growing usage restrained by a fixed cap, but identical arguments apply to Ethereum as well.

Game-Theoretic Attacks

There is also another argument to bolster the case for inflation. This is that relying on transaction fees too much opens up the playing field for a very large and difficult-to-analyze category of game-theoretic attacks. The fundamental cause is simple: if you act in a way that prevents another block from getting into the chain, then you can steal that block’s transactions. Hence there is an incentive for a validator to not just help themselves, but also to hurt others. This is even more direct than selfish-mining attacks, as in the case of selfish mining you hurt a specific validator to the benefit of all other validators, whereas here there are often opportunities for the attacker to benefit exclusively.

In proof of work, one simple attack would be that if you see a block with a high fee, you attempt to mine a sister block containing the same transactions, and then offer a bounty of 1 BTC to the next miner to mine on top of your block, so that subsequent validators have the incentive to include your block and not the original. Of course, the original miner can then follow up by increasing the bounty further, starting a bidding war, and the miner could also pre-empt such attacks by voluntarily giving up most of the fee to the creator of the next block; the end result is hard to predict and it’s not at all clear that it is anywhere close to efficient for the network. In proof of stake, similar attacks are possible.

How to distribute fees?

Even given a particular distribution of revenues from inflation and revenues from transaction fees, there is an additional choice of how the transaction fees are collected. Though most protocols so far have taken one single route, there is actually quite a bit of latitude here. The three primary choices are:

  • Fees go to the validator/miner that created the block
  • Fees go to the validators equally
  • Fees are burned

Arguably, the more salient difference is between the first and the second; the difference between the second and the third can be described as a targeting policy choice, and so we will deal with this issue separately in a later section. The difference between the first two options is this: if the validator that creates a block gets the fees, that validator has an incentive equal to the size of the fees to include as many transactions as possible. If it’s the validators equally, each one has a negligible incentive.

Note that literally redistributing 100% of fees (or, for that matter, any fixed percentage of fees) is infeasible due to “tax evasion” attacks via side-channel payment: instead of adding a transaction fee using the standard mechanism, transaction senders will put a zero or near-zero “official fee” and pay validators directly via other cryptocurrencies (or even PayPal), allowing validators to collect 100% of the revenue. However, we can get what we want by using another trick: determine in protocol a minimum fee that transactions must pay, and have the protocol “confiscate” that portion but let the miners keep the entire excess (alternatively, miners keep all transaction fees but must in turn pay a fee per byte or unit gas to the protocol; this a mathematically equivalent formulation). This removes tax evasion incentives, while still placing a large portion of transaction fee revenue under the control of the protocol, allowing us to keep fee-based issuance without introducing the game-theoretic malicentives of a traditional pure-fee model.


The protocol cannot take all of the transaction fee revenues because the level of fees is very uneven and because it cannot price-discriminate, but it can take a portion large enough that in-protocol mechanisms have enough revenue allocating power to work with to counteract game-theoretic concerns with traditional fee-only security.

One possible algorithm for determining this minimum fee would be a difficulty-like adjustment process that targets a medium-term average gas usage equal to 1/3 of the protocol gas limit, decreasing the minimum fee if average usage is below this value and increasing the minimum fee if average usage is higher.

We can extend this model further to provide other interesting properties. One possibility is that of a flexible gas limit: instead of a hard gas limit that blocks cannot exceed, we have a soft limit G1 and a hard limit G2 (say, G2 = 2 * G1). Suppose that the protocol fee is 20 shannon per gas (in non-Ethereum contexts, substitute other cryptocurrency units and “bytes” or other block resource limits as needed). All transactions up to G1 would have to pay 20 shannon per gas. Above that point, however, fees would increase: at (G2 + G1) / 2, the marginal unit of gas would cost 40 shannon, at (3 * G2 + G1) / 4 it would go up to 80 shannon, and so forth until hitting a limit of infinity at G2. This would give the chain a limited ability to expand capacity to meet sudden spikes in demand, reducing the price shock (a feature that some critics of the concept of a “fee market” may find attractive).

What to Target

Let us suppose that we agree with the points above. Then, a question still remains: how do we target our policy variables, and particularly inflation? Do we target a fixed level of participation in proof of stake (eg. 30% of all ether), and adjust interest rates to compensate? Do we target a fixed level of total inflation? Or do we just set a fixed interest rate, and allow participation and inflation to adjust? Or do we take some middle road where greater interest in participating leads to a combination of increased inflation, increased participation and a lower interest rate?

In general, tradeoffs between targeting rules are fundamentally tradeoffs about what kinds of uncertainty we are more willing to accept, and what variables we want to reduce volatility on. The main reason to target a fixed level of participation is to have certainty about the level of security. The main reason to target a fixed level of inflation is to satisfy the demands of some token holders for supply predictability, and at the same time have a weaker but still present guarantee about security (it is theoretically possible that in equilibrium only 5% of ether would be participating, but in that case it would be getting a high interest rate, creating a partial counter-pressure). The main reason to target a fixed interest rate is to minimize selfish-validating risks, as there would be no way for a validator to benefit themselves simply by hurting the interests of other validators. A hybrid route in proof of stake could combine these guarantees, for example providing selfish mining protection if possible but sticking to a hard minimum target of 5% stake participation.

Now, we can also get to discussing the difference between redistributing and burning transaction fees. It is clear that, in expectation, the two are equivalent: redistributing 50 ETH per day and inflating 50 ETH per day is the same as burning 50 ETH per day and inflating 100 ETH per day. The tradeoff, once again, comes in the variance. If fees are redistributed, then we have more certainty about the supply, but less certainty about the level of security, as we have certainty about the size of the validation incentive. If fees are burned, we lose certainty about the supply, but gain certainty about the size of the validation incentive and hence the level of security. Burning fees also has the benefit that it minimizes cartel risks, as validators cannot gain as much by artificially pushing transaction fees up (eg. through censorship, or via capacity-restriction soft forks). Once again, a hybrid route is possible and may well be optimal, though at present it seems like an approach targeted more toward burning fees, and thereby accepting an uncertain cryptocurrency supply that may well see low decreases on net during high-usage times and low increases on net during low-usage times, is best. If usage is high enough, this may even lead to low deflation on average.

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Vitalik Buterin

https://ethereum.org

Comments
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Author miki miki

Posted at 5:33 pm July 27, 2016.

Boring…

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Author wighawag

Posted at 5:35 pm July 27, 2016.

Since ethereum is not meant for financial transaction only, a transaction fee is not ideal. I would rather see ethereum get rid of transaction fee. Steem does it by rate limiting tx per address based on their balance.
What do you think?
I created an EIP on that here : https://github.com/ethereum/EIPs/issues/135

Basically tx fees has 2 roles in the current system : reward miners and block abuse.
I think these 2 concerns should be separated.

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Author David Jerry

Posted at 5:46 pm July 27, 2016.

“but then the size of transactions conducted over the network will also increase and so the incentive to attack will also increase”

Why? This attack you are hypothetically speaking of is a 51% attack to double spend or perhaps to clog the network. I don’t see how the #txns being processed on it has any bearing on the attack incentives.

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Author Garrick Hileman

Posted at 6:22 pm July 27, 2016.

Hi Vitalik,

Regarding your point “In 25 years, bitcoin mining rewards are going to almost disappear”, that is correct in terms of the actual nominal amount of bitcoin received for the mining reward.

However, the $ value of the bitcoin reward is unknown as we don’t know what the price of bitcoin will be in 25 years. In other words, if bitcoin’s exchange rate significantly appreciates then the effective fiat value of the mining reward in 25 years could still be quite significant.

Garrick

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    Author ciaranmurray

    Posted at 4:23 pm July 28, 2016.

    It is assumed that with adoption the price of bitcoin will appreciate. However the cost of mining will do so concurrently. That is the trend we have seen from its inception.

    Reply
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    Author Leathan Axe

    Posted at 5:28 pm August 13, 2016.

    this was so wrong i had to stop reading. . . no srsly dont ninja fork it pl0x.

    Reply
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Author Zack Hess

Posted at 8:20 pm July 27, 2016.

Hi Vitalik Buterin,

Thank you for explaining the ramsey thing, and making these estimates. Now I have a hope of tuning my blockchain.

Instead of inflation we should charge rent based on how many bytes of consensus space each user is using, and pay validators from this.
Storing an account with twice as much money in it costs the same amount of resources.
We should not subsidize people who want to split their money into lots of tiny accounts.

If you split proof of stake bonds into 2 types, then it can be secure with much less “defense spending”.
https://github.com/BumblebeeBat/FlyingFox/blob/master/docs/2_types_of_bonds.md

“Defense spending” is not the number of importance for comparing blockchains.
Instead we should pay attention to “security efficiency”, (the cost to attack) / (the cost to defend)

which I write about here: https://github.com/BumblebeeBat/FlyingFox/blob/master/docs/2_types_of_bonds_calculation.md

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Author veox

Posted at 9:14 pm July 27, 2016.

“so the cost becomes $4.08 USD” – you meant $4.08 million USD.

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Author hawks5999

Posted at 9:27 pm July 27, 2016.

Vitalik, I think Ethereum faces a big risk by being associated with Coinbase who is talking a lot about their support for ETH but don’t seem to be able to process a simple deposit of ETH. Anybody thinking of doing any sort of financial activity with Ethereum should probably have some great fear because of any association with Coinbase. It makes the whole currency seem kinda scammy now to be honest.

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    Author bruno cecchini

    Posted at 9:45 pm July 29, 2016.

    The post is about fee not about Eth

    Reply
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Author sLy5aM

Posted at 3:16 am July 28, 2016.

bla bla bla… nobody is listening..

trust is gone

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    Author Christian Seberino

    Posted at 7:12 am July 31, 2016.

    So sad but so true.

    Reply
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    Author Shakedog

    Posted at 10:51 pm August 7, 2016.

    The market is a better indication of sentiment than social media rhetoric. I disagree 110%.

    Reply
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Author Alexandre PAYNEAU

Posted at 8:29 am July 28, 2016.

Fair approach Vitalik! I agree with your proposal of scalability.
Beyond the cryptocurrency model only, I would say it’s kind of “trap of engineering” to focus only this matter to compensate the effect of inflation/deflation and keep a high level of security. (Reference is made American Ice Company which collapse in 19th).
Another way have not been explored, called the diversification. the world of cryptocurrency will be always influenced by social behaviour. Leading those social behaviour in the proper way would have a positive impact on the problem you are trying to solve. See Google, it’s not anymore

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Author Mystisfication

Posted at 12:11 am July 31, 2016.

Thanks for your insight Vitalik!

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Author Blindfolded

Posted at 7:05 pm August 1, 2016.

In 25 years, bitcoin mining rewards are going to almost disappear; hence, the 0.35 BTC per block will be the only source of revenue. We can estimate the cost of buying up enough mining power to take over the network given these conditions in several ways.

So…you’ve extrapolated the future 25yrs out by applying CURRENT transfer fees to a CURRENT bitcoin price, then used a CURRENT hashing power and CURRENT processor costs to make a case that BTC in 25yrs after inflation largely subsides, as a a FEE only network, won’t pay enough for security?

Then you’ve based your entire flawed security analysis on this flawed forecast…so that you can…

…suppose that relying purely on current transaction fees is insufficient to secure the network.

…which is a false narrative, because you’re using current statistics from a network incentivized by block reward (BTC), to provide false (inconsistent) justification that a fee only network won’t have enough security…and so that you can state…

it is my own opinion that the risk is very high that this is insufficient

…so that you can discuss…

(There are) two ways to raise more revenue. One is to increase transaction fees by constraining supply to below efficient levels, and the other is to add inflation. How do we choose which one, or what proportions of both, to use?

What about the third option…increase the # of transactions…increase the size of the pie from which transactions fund security.

Seem to me, your whole article can be debunked by first pointing out that your whole analysis relies on your reliance upon using a current bitcoin price ($625)…25yrs in the future(?!?)…to project insufficient security funding for the BTC blockchain 25yrs in the future. Even if one was to believe that transfer fees remain at 0.35btc/block, you’d have to drink the kool aid to believe BTC will be worth $625 in 25yrs.

Lets must take Wedbush’s analysis of BTC price for example. 10yrs they forecast it at $17,800/btc. Those 0.35btc/block render $897,120/day and $327m/yr, which throws your entire security analysis of Fee Only networks in the wash.

Lastly…look at this chart and tell me if you think BTC transaction fees will remain at “~$35000 per day or $10 million per year” for the next 25yrs.

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Author Alexandre PAYNEAU

Posted at 7:47 am August 2, 2016.

Hi Vitalik,
ETH:3365.6 GH/s, ETC:834.9 GH/s some minute ago

I would like to help you, and like to share the following article form HBR.
https://hbr.org/2016/08/until-you-have-productivity-skills-productivity-tools-are-useless?utm_campaign=HBR&utm_source=linkedin&utm_medium=social

The Tool is the Blockchain and useless as per article, if it’s not associated to a Rules of the Game.
I Believe that you will take this opportunity to differentiate ETC/ETH. You are the Guy with the VISION, and people doesn’t need to understand the mechanic of the tool to play a game.

Your above analitic is fair and must provide the conditions to scale Ethereum to the Majority. The more you get these rules clear, the more you will commit people to embrace this technology in their day to day life.

A contrario, if you let thing unclear such as it is now, people will get confused and it will be the gate opened for all the populist ( extremist ). From the anarchy there is always an issue, the decision is your.

I wish you the best to succeed.

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    user

    Author Leathan Axe

    Posted at 5:37 pm August 13, 2016.

    EF=Education First right?

    Reply
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      Author Leathan Axe

      Posted at 5:39 pm August 13, 2016.

      That’s what I was told when i FORKED OVER THIRTY THOUSANDS UNITED STATES FEDERAL RESERVE NOTES.

      it all poofed now says my bank =( pparantly im crazy.

      EDIT: I have the receipt lulz.

      Reply
        user

        Author Leathan Axe

        Posted at 5:51 pm August 13, 2016.

        Are we allowed to bump? if so ill delete my comments and organize them into 1.

        Reply
        user

        Author Leathan Axe

        Posted at 5:54 pm August 13, 2016.

        I guess i got an ipad… but after i jailbroke it they stuck me in jail so i broke it and then sold the broken pos.

        EDIT: LULZ

        Reply
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Author Hsun Yang

Posted at 10:14 am August 12, 2016.

Hi Vitalik,

I am playing with private chain on geth console recently and it says that we have to wait for 5 confirmations to ensure a block is not reversible. However, according to your post “On Slow and fast Block Times”, it says that more confirmations are needed for serious events such as economic trading. I’ve wondered that if we set a rule that the newly mined block could not be attached to block that is considered too “old”, let’s say 5 blocks old. So every block with 5 more blocks attaching to it will be considered as “never-reversible”. Is there any disadvantage of setting such rule to reduce the time waiting for confirmations? Or what are the advantages of allowing miners to mine on any block of main chain so that there’s a chance to reverse a confirmed block?

Hsun

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Author Leathan Axe

Posted at 5:27 pm August 13, 2016.

Hello I like u alot please code more talk less =)

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    user

    Author Leathan Axe

    Posted at 5:29 pm August 13, 2016.

    WOOOOOOOOOOOOOOOOOOOOOOT IM UN DOUBLE IPV4BANNED

    Reply
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Author José

Posted at 2:22 pm August 18, 2016.

In my humble opinion, for this tech to achieve “world changing” status, it needs to create critical mass, the many more people who uses the “underlying tech (ethereum)” the more secure it will be. Now if you allow big players to get in and take over the “network” I believe that will be a game ender. the power of this tool is in if everyone mass adopts it. everyday transactions buy coffee or vegetables, easy, private etc.

forget the internet. this will create a new world order. I’m just blown away with the possibilities of all this!

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Author Brian Ahier

Posted at 8:44 pm September 4, 2016.

Great post! On a side note, do you see possibilities for ethereum to be used in healthcare in a similar way that blockchain is being explored?

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Author Eddie J

Posted at 7:25 am September 13, 2016.

Hi, So you mean to say convince the four largest Chinese mining pools to rent you their hardware. Adding, to take control of the product they collectively secure. Unless you are actively making an accusation against the current bitcoin miners, the underlying argument is only a sales tactic. The counter argument being complexity has left Ethereum split. I’m wondering who will be first to proof of stake and have the better execution.

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Author Kevin Korbien

Posted at 4:45 am September 15, 2016.

Did you guys see this? Could be the killer app for Ethereum if entire Aviation industry goes blockhain. https://buyingbusinesstravel.com/news/1326220-special-report-airlines-prioritise-digital-strategy

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Author Chih-Cheng Liang

Posted at 7:55 pm October 11, 2016.

Hi Vitalik,
I’m not certain if the following quoted sentence express what you want to say.

If fees are redistributed, then we have more certainty about the supply, but less certainty about the level of security, as we have certainty about the size of the validation incentive.
Should it be “as we have less certainty about the size of the validation incentive.”?

btw, just for fun, I’m trying to translate this great article for people in Taiwan. https://docs.google.com/presentation/d/1tTj5a-wUIpSAG7FQ_V1g0oG8qh73qAiTbFUlmFxffeg/edit#slide=id.g1680bb13a1_0_126

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