'Conciliation' of the reward curves? / Die 'Versöhnung' der Reward-Kurven?

in steemit •  last year

English (deutsche Übersetzung unten)


Advantages and disadvantages of a linear reward curve compared to n^2.


The question which of the reward curves is better, n^2 or a linear one of the most discussed here on Steemit. Just recently @dan emphasized again, that he clearly is in favor of a non-linear curve, while @ned commented to be convinced of the opposite.

Actually both curves are having advantages and disadvantages:

  • Because of its flat beginning n^2 discourages self-votes on articles and especially also comments on which nobody else is (or only very few are) voting. However the disadvantage is, that it leads to extreme rewards for posts which receive a big amount of upvotes.
  • A linear reward curve doesn't have the disadvantage of n^2. However upvoting own comments (or articles with few other upvotes) is now much more attractive than before.

Would a sigmoid reward curve be a suitable solution?


One try to solve both problems with one single function would be to use a sigmoid reward curve. Due to it's flat begin it would be far less attractive to upvote posts on which nobody else is voting (self-voting of comments would be less attractive). As it also ends flat, extreme rewards (other than with n^2) would be avoided, as well.
It was @twinner who mentioned this idea, and I still think it would be an interesting solution. One problem could be that graphs of sigmoid functions are approaching a limiting value so that finally further upvotes nearly wouldn't have any effect anymore.

What about 'conciliating' (combining) both curves?


Thinking about all that I got a new idea. Before presenting it let me emphasize that ideas are there to be either further developed if others find them to be interesting, too, or to be discarded in case they are just unfeasible. I am well aware that my idea may have some flaws I am not yet aware of or may be just too complicated to implement (which I doubt).

So what about if the reward curve started as y = n2 with a flat beginning (against self-votes) and a steep slope afterwards? Then, after "n" had exceeded a certain value, the curve could become linear (y = m·x + b; where for example m = 1 and b gets allocated exactly that value that the next y-value will be one unit higher than the previous y-value, so that there is no interruption of the incline of the curve). The advantage of the linear ending would be to avoid extreme rewards (like n^2 causes) but at the same time having no limiting value like a sigmoid function.

Such a curve could look like this (that's just an example, it's the idea which matters - I am just an ordinary Steemit-user giving the implementation into the hands of professionals who are getting paid for doing things like that. :-)))

Deutsch


Vor- und Nachteile der linearen Reward-Kurve verglichen mit n^2.


Die Frage, welche der beiden Reward-Kurven, n^2 oder linear, die bessere sei, ist eine der meist diskutierten hier auf Steemit. Gerade erst kürzlich betonte @dan erneut, dass er ganz klar eine nichtlineare Kurve bevorzugt, während @ned kommentierte, vom Gegenteil überzeugt zu sein.

Letztlich sind mit der Implementierung beider Kurven sowohl Vor- als auch Nachteile verbunden:

  • Aufgrund ihres flachen Beginns ist n^2 ein gutes Mittel gegen Selbsvotes von Artikeln und besonders auch Kommentaren, die bis dahin von niemand anderem (oder nur sehr wenigen) upgevoted wurden. Allerdings besteht der Nachteil darin, dass es im Falle sehr zahlreicher Upvotes zu extremen Rewards per Post kommen kann.
  • Eine lineare Kurve weist diesen Nachteil von n^2 nicht auf. Allerdings begünstigt sie das Upvoten eigener Kommentare (oder Artikel mit wenigen anderen Upvotes).

Wäre eine sigmoide Reward-Kurve eine sinnvolle Lösung des Problems?


Einen Versuch, beide Probleme mit einer einzigen Funktion zu lösen, stellte die Nutzung einer sigmoiden Reward-Kurve dar. Ihres flachen Beginns wegen wäre es viel unprofitabler, Posts upzuvoten, die ansonsten keine anderen Upvotes erhielten (eigene Kommentare zu voten wäre weniger attraktiv). Da sie außerdem auch flach endet, würden extreme Rewards (anders als bei n^2) ebenfalls vermieden.
Es war @twinner, der diese Idee erwähnte, und ich halte sie immer noch für eine interessante Lösung. Ein Problem dabei könnte sein, dass sich die Graphen von Sigmoidfunktionen einem Grenzwert annähren, so dass schließlich weitere Upvotes fast keinen Effekt mehr hätten.

Wie wäre es damit, beide Kurven miteinander zu 'versöhnen' (sie zu kombinieren)?


Während ich über all das nachdachte, kam mir eine neue Idee. Bevor ich sie euch vorstelle, möchte ich betonen, dass Ideen dazu da sind, weiterentwickelt zu werden, wenn andere sie ebenfalls interessant finden oder verworfen zu werden, falls sie sich als undurchführbar erweisen. Mir ist bewusst, dass meine Idee möglicherweise Schwachstellen hat, die ich nicht berücksichtigt habe oder vielleicht zu kompliziert zu implementieren ist (was ich eher nicht vermute).

Also, wie wäre es damit, die Reward-Kurve als y = n2 mit flachem Beginn (gegen Selbstvotes) starten und danach steil ansteigen zu lassen? Dann, nachdem "n" einen bestimmten Wert überschritten hat, könnte sie in eine lineare Funktion übergehen, z. B. y = m·x + b; wobei zum Beispiel m = 1 sein könnte, und b genau den Wert zugewiesen bekäme, dass der folgende Y-Wert eine Einheit höher wär als der vorherige Y-Wert, so dass der Anstieg der Kurve nicht unterbrochen wäre). Der Vorteil des linearen Endes der Kurve wäre es, extrem hohe Profite (wie sie n^2 verursacht) zu verhindern, aber zugleich keinem Grenzwert zuzustreben wie eine sigmoide Funktion.

Solch eine Kurve ist oben abgebildet. (Es handelt sich dabei nur um ein Beispiel - es ist die Idee, um die es mir geht; ich bin nur ein gewöhnlicher Steemit-Nutzer, der die Implementierung gerne den Experten überlässt, welche dafür bezahlt werden, so etwas zu tun. :-)))

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Gutes Thema zu dem ich allerdings nicht wirklich was beitragen kann. Dennoch klingt deine Kombination aus beiden Kurven recht interessant. Ob das aber die Mehrheit auch so unterstützen würde? 🤔
Upvoted... 👍

Ds ist eine gute Idee. Man könnte nun auch noch den Knick vermeiden, indem man mit der Geraden dort beginnt, wo die Parabel exakt ihre Steigung besitzt. Dann wäre sie nicht nur stetig, sondern stetig differenzierbar, wie der Mathematiker zu sagen pflegt. Bringt man weiter nicht nur die erste, sondern auch noch die zweite Ableitung zusammen, erschiene sie noch glatter. Das führt uns zur Spline-Interpolation, bei der abschnittsweise stetig differenzierbare Kurven möglichst glatt zusammengefügt werden. Man könnte also statt zwei sogar drei oder mehr Abschnitte in die Rewardkurve einbauen, wenn man dafür einen bestimmten Zweck hätte.

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Das ergibt sicher eine schöne Kurve, aber wie ist das ganze denn skaliert ?

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Dazu kann ich leider nichts beitragen, weil ich die aktuellen Einstellungen nicht kenne.
Mathematiker liefern ohnehin nur die Konzepte, Ingenieure wenden sie an. Somit bin ich exkulpiert.

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Danke für deine obigen Ausführungen!
Wie das Ganze skaliert werden sollte, ist - wie ich @felixxx auch schrieb - m. E. eher eine politische als eine mathematische Frage ...

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Die Kurven derzeit kommen ohne Knick aus ...

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Der schicke Knick, welch' Missgeschick, bricht der Idee noch das Genick?

Wie 'schlimm' ist der Knick? :) (Ich denke, wenn er das einzige Problem wäre, sollten wir meine Idee unverzüglich umsetzen!)

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Ich komm mal am WE in den Steemit.chat und schau mir das an. Ohne mich ist das ja letztes mal gut in die Hose gegangen :P

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4x! 4x! Ich hab die Lösung!....Ehm ich mein, wenn man die Steigung der Kurve übernimmt, wäre aber jede Vote nach der 19 stärker als alle zuvor, also genau das was ich nicht haben will.

Ich kenn zwar die Spline-Interpolation nicht, aber "Stetigkeit" ist schon ein Trigger Wort für mich, so trivial und trotzdem so schwer zu zeigen.

Find ich eine ganz gute Idee von dir, jedoch denke ich die Sigmoiden-Funktion kommt deiner Idee ganz nahe. Wenn ich daran denke, dass jemand schon 400 Upvotes hat und einen ordentlichen Wert, ich denke da sollte schon eine Grenze sein, die der Wert nicht überschreiten kann. Schließlich soll das Ganze reglementiert sein und nicht ins Unermessliche steigen können.

Gruß Naturicia

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hmm mit dem Gedanken einer Reglementierung ist hier kaum ein Blumentopf zu gewinnen.
Daher kann man die sigmoide Funktion vergessen, da wird sich niemals die Mehrheit der Witnesses und Stinc drauf einigen...

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Ja, das könnte gut sein ...

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Ich finde die Idee einer sigmoiden Kurve ziemlich gut, aber ich vermute, @jedigeiss hat Recht damit, dass sie keine Mehrheit finden würde ...

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So ist es, die schneiden sich doch nicht ins eigene Fleisch um weniger zu verdienen ;-) Ich kenne hier auf Steemit nur sehr wenige, die nicht das System volles ausschlachten, obwohl sie es mit ihrer SP gnadenlos machen könnten. Guter Bericht lieber @jaki01

In the meanwhile I found an older, but very interesting article of @clayop.

Like I said before:

Where exactly would you want the slope to start declining ?
This is not a trivial question, at all.

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I still don't 'want' anything. :) In case responsible Steemians would find my idea to be interesting (which is an essential condition for me to be ready to invest more time to explore the necessary details) I would think more thoroughly about that. It would be primarily a question at which point we would like to limit the increasing rewards - so it would be more of a political than a mathematical decision.

I agree with you that it's not a trivial question.

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It all boils down to game theory.
Therefore it is a mathematical question.

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It is also a question about what the community wants ...
For example if everybody agrees that very successful accounts should earn as much as possible, there shouldn't be any linear ending at all. If the majority thinks that earnings may be somewhat exagerated, there should be one. The earlier n² is replaced by a linear equation the more equal the rewards distribution will be. If it is too early, it will be very profitable again though to upvote own comments ...

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I disagree.
The protocol should always be set up in such a way, that it requires the least amount of trust.

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You have to define 'trust' (in what?).

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Trust in the other parties, using the same protocol.

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Of which parties are you talking? (Sorry for being ignorant maybe ...)

good post @jaki01, i definetly see the need to act in some way as well. The idea proposed in your post would really help with the situation that we are currently facing, the only thing missing is a flagging solution, in which i would propose to take a n² curve:) then the flags would, if really many flags would come together, be taken really serious.
Thanks @Jaki01!
Jan

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Ich weiß nicht, inwiefern das schon behandelt wurde, aber @Transisto hat heute einen Vorschlag zum Flagging System gemacht, in dem er sich für einen 2. separaten 'power pool' einsetzt.
Flagging würde somit nicht bzw. weniger die eigene voting power beeinflussen. Stattdessen wird etwas von der 'downpower' abgezogen.
Vielleicht schaust du da mal vorbei Jan.

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Hm, ich bin mir nicht so sicher, wie ich das einschätzen soll: Es würde einerseits helfen, gegen Spammer etc. vorzugehen, andererseits würde es großen Accounts leichter gemacht, kleinere - z. B. bei abweichender Meinung - 'mundtot' zu machen ...

u have some interesting points here

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I am glad to see that you appreciate my thoughts and also are contributing to make my post a little bit more visible!

Ich finde es toll durch deine Artikel immer einen Einblick in Themen zu bekommen in die ich sonst wahrscheinlich nicht eingetaucht wäre :)
Ich werde mich gleich mal noch etwas durch die Kommentare fuchsen. Danke fürs teilen des Artikels und die Themengebiete :))

aber wartet mal. Vergessen alle auf einmal dass die großen Fische tausende von Alts und Sockpuppets haben? N² favorisiert imo klar die technisch versierten unter uns und ist nicht sehr einsteigerfreundlich.

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n^2 favorisiert einzelne, starke accounts statt sock-puppets.

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Wieso das? 3 starke Votes sind doch weniger Wert als 30 Schwache mit n²

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Genau deshalb soll n^2 ja auch ab einer bestimmten Vote-Anzahl gemäß meinem Vorschlag in eine lineare Kurve übergehen ...

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aber gerade diese Hürde wäre für einen kleinen/neuen User schwer zu nehmen. Die Großen schaffen es auf eine gewisse Anzahl von Votes so oder so.

Wobei wenn man es nun wirklich mit n² machen würde und nicht wie bei dir im Bild mit 0.1n² , dann würden die ersten Votes am meisten zählen... vllt ist da doch was dran. Aber auch dann sehe ich einige Probleme auf uns zukommen

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Auch bei n^2 zählen - auf mein Beispiel übertragen - die mittleren Votes mehr als die anfänglichen, bis dann die lineare Funktion übernimmt. n^2 würde aber schon am Anfang genauso stark steigen wie linear (deshalb das Beispiel mit 0,1*n^2). Das Ganze ist aber sowieso vereinfacht dargestellt, denn zusätzlich gibt es ja derzeit noch das 30-Minuten-Vote-Fenster.

Auf eine mittlere Anzahl von Votes sollte man also schon kommen, was aber bei konstant guten Artikeln möglich sein dürfte. Der Start mit n^2 hätte halt den Vorteil, Selbstvotes weniger attraktiv zu machen.

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Wie gesagt ich denke die technisch versierten werden es schaffen diese Hürde zu umgehen.

Das einzig Gute was ich sehe, ist die potentielle umverteilung, da kleine-mittlere Posts mehr und die großen Posts (mit 200+ upvotes) weniger bekommen.

Ein Problem was ich hier sehe ist, dass es dann für die Großen viel mehr Anreiz gibt zu spammen: Wenn sie ihre 200 Votes von einem Post auf 10 Posts mit 20 Votes verteilen, wäre das wahrscheinlich profitabler.

Hört sich aufjedenfall machbar und garnicht so verkehrt an! Im Moment läuft vieles doch noch nicht ganz rund hier... Aber wird von Tag zu Tag immer besser!

Sigmoid might make sense, although I don't know how popular a solution it would be. I figure anything that caps post value, effectively, would be frowned upon by a large segment of the steemit population - but at the same time, that sort of "regulation" might also help stabilize the platform for mass appeal.

This might all be a spit in the wind as ned has just recently dismissed non-linear reward curves in a comment on dan's recent post - and seemed to think quite highly of linear rewards.

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Exactly because a sigmoid curve probably won't be accepted, and also because @ned favors a linear 'curve', I made my suggestion to combine n^2 with a linear function!

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Right - but it seems like ned doesn't think things need to be changed at all - which seems contrary to a long term picture for the platform if mass adoption is actually a goal - but that's where it's at atm by the looks of it.

Having said that, the way you describe it, the n^2 into linear curve sounds appealing - I'm just not sure there is top down interest in changing the curve, period.

Very nice article and also very useful Sir @jaki01, steemit as a user I think we do need to know about these ideas, especially above there is a difference of opinion of the officers of the steemit between @dan and @ned. Of course I also don't turn away from the idea that you ask Sir @jaki01, roughly what the advantages are essentially for novices like me this steemit if using methods from you Sir, like y = n², because basically I see your idea provided in the form of the curve increases any more stable without any extreme awards as an example of the idea of the other.

Sehr interessante Gedanken zur Problemlösung.
Eine Kombination der Reward Kurven hört sich zunächst für mich sehr interessant an.
Zur genauen Umsetzung kann ich da wenig beitragen.
Aber schön, dass sich bezüglich Systemverbesserung ausgiebig Gedanken gemacht werden!

@jaki01 - Sir the reward mechanism you proposed can be the best suggestion than n^2 or linear reward mechanism... Nice you decided to introduce this method Sir... Really appreciate your contribution...

+W+

@jaki01,
You got the point! Yeah deduct self-upvotes is a must, but with n^2 it has it's own disadvantages as you said. So better after a certain time it might be back to linear model!
Please propose this to the HF20 discussion forum! Hope @ned will check the suitability of this proposal!
After all I feel you are a mathematician! For me this is impossible to think!

Cheers~

Brilliant idea, and certainly sounds like it could help matters, but I do agree with @dan's point that the lack of transparency incentivizes some underhanded behavior.

Combining reward theory looks better than @ned & @dan 's proposed theories.


Hope they will think to implement this one.

~Followed & Upvoted

very interesting stuff.

Excellent reward curve advantages & disadvantages mathematics. Thanks for sharing us.

excellent writing @jaki. thanks for sharing

hey @jaki. Whenever you read, you can learn something new. We benefit from each of your writing.
thanks for sharing

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Why did you upvote your comment but not the article?

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Buy Steam Power. We voted after buying. Which one is good

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Who is 'we'? And if you bought Steem power why your upvote is worth 0 USD? Anyway: thanks for upvoting now! :)

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After that, it will not be so. I thought you might not read so much below. But my guess is wrong. You are really good.
thanks

This is very important information & good post
Thanks @jaki01
Have a nice day

Nice writing @jaki01
I like this post
Thank you for your information

Good article dear friend

Very knowledgeable post, thanks for it

a linear one seems to be a suitable one after understanding

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Linear alone makes it very attractive for big accounts to upvote their own comments ... Therefore I suggested this combination.

interesting topic to debate on for sure would be looking forward for community feedback on this

time to solve the equations

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Oh, it's not a riddle this time ...

i understand linear is way better

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Linear alone makes it very attractive for big accounts to upvote their own comments ... Therefore I suggested this combination.

that's why i hated math in my entire life but it seems important here

nice thing to know but not an expert on this thanks for sharing

both the ideas are great but for long term we need an expert

Excellent writing experience
100% like and resteem

Great article my friend.. I have taught Maths for about 4,5 years... And I can say that great mathematical explanation... Are you a mathematician??

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No, but I like mathematics. :)
By the way, if you like the article, you actually may consider to upvote it. :)

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Dear I wanted to upvote you but my SP is so low... you can see.. and at that time VP was also low... So, here comes a tinny minny upvote from a minnow... :)

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Don't worry, I appreciate your upvote a lot (it 's the gesture that matters). :)

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Yap you are right and thank you so much....

advantage seems to be cool in this

Thank you for posting @jaki01, adding to my knowledge as a mathematics teacher who is always associated with curves like this

seems like we need some great steemians for this resteemed

This is how maths help Steemit. Excellent proposal & incredible solution. It answer both problems at the same time. Hope this is the best solution than n^2 or linear~

Nice post with so much complex calculations

Hats off @jaki01 for writing this article I did not knew about this... Missing your chess blog please make a blog on chess!!

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Check @iceblue. He is a friend of mine and just recently also made a chess riddle. :)

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Okkk thanks for suggesting @jaki01!!

Very nice.. Cool 👍

Hello @jaki01,

Extraordinary good thought. n^2 to linear. Hope you submit this proposal to HF20 :)

~@mywhale

Vielen Dank für Sie teilen Artikel über die Kurve. Bevor ich mich entschuldige. Kann nur sagen, erstaunt mit Ihrer Idee, weil ich nicht über die Kurve wissen. Und ich sehe in dem Artikel, dass Sie teilen so viel über die Natur.

Wenn Sie nicht wie der Artikel Tier-kleine Tiere? Wenn Sie möchten, besuchen Sie meine Web lah. Es kann von Interesse sein, Sie Dank

combining graphs is a good idea. it can answer less drain reward pool & limit self upvotes at the same time. impressive concept @jaki01

@resteemia
reteemed & upvoted & commented & followed

@jaki01
Such a great article and thanks for sharing.

good post @jaki01.really helpful article sir
Resteem

That is valuable post. great writing experience @jaki01

For your post propagation.
Upvote/Resteem

Very good idea brother ...
I agree with brother ... @jaki01

True what Mr. @jaki01 said, that his own comment upvoting (or articles with a few more upvotes) now much more attractive than ever. According to Mr. @jaki01 of the curve where the more interesting??

I very much agree with you. Because by doing so could increase the wages of those account users. @jaki01

i see know how it works , the reward mechanicsm.
I barely can understand that.

it s great if you have some new idea to improve it.
Hope they can considered it.

I simply understand about rewards as the following picture ,sir

rY82Gk7.jpg

Very Excellent Thanks for sharing bro : D

I'm happy with the flat reward curve, at least my vote is worth something and the ones I get are worth something. That's why I came back to Steemit.
For the platform to grow you need more people, a curved reward distribution will discourge new users. Don't expect someone to sign up and know how things work, because I sure didn't.

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Your vote counts more because of the fourfold heavier weight (since the last hard fork) in case you use 100 % of your voting power ... By the way, a linear reward curve isn't "flat". :)

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Linear , flat, straight, whatever...you know what I mean. Fourfold heavier weight? I didn't know about it, which brings me back to my point that you can't expect somebody in jump in here and know what they are doing or what's going on.

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Nobody will forbid you to inform yourself about "what's going on". :)

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Well my proposal would be for Steem to become a POS coin, payouts are made according to one's Steem Power. When you vote for a post it comes out of your own pocket. "Self voting" would be neutral and a lot of crap wouldn't be posted.

How about taking user reputation into account while calculating rewards?

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@scipio made some suggestions going into this direction. His concept is based on UserAuthority.

I think linear is best, it is simple, understandable, and fair, and also helps minnows to get a bit recognition.

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Linear alone makes it very attractive for big accounts to upvote their own comments ... Therefore I suggested this combination.

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I see, I think these are two separate issues, reward curve and self voting. I would keep the reward curve linear and perhaps address the self voting issue for big accounts in a different way, if at all. For example, we could limit the number of self votes per day or introduce a cap for the value of a self vote, what do you think?

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It wouldn't help, because most big account holders have at least a few accounts. And of course also the reward curve plays a role when it comes to the question how lucrative self-voting is.
If you are interested you may read one of my older articles about the self-voting topic here.

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A non-linear reward curve does not solve the fake account attack vector too. A corrupt whale can create multiple accounts and upvote his own content, even profiting from a non-linear curve with that. I still prefer linear.

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... But then he must spread his voting power over several accounts and 'waste' some voting power before n^2 is getting effective ...

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New conclusion, maybe we have to live with that, it is similar in real life too, a billionaire has more power than a normal citizen. If it is acceptable for a minnow to upvote oneself than it is probably also acceptable for a whale to do that ;)

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Useful and informative post thank you dear friend @jak01

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If the post is "useful" you actually may consider to upvote it. :)

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This is a very special topic. Thank you very much for this

Your post is very classy and quality.
I like this post.
thanks for sharing

Nice information .... Thanks for share this

Bagus s

was wäre wenn man zusätzlich noch einen algorhytmus einbauen würde der erst nach einer gewisser zeit anzeigt wie viel upvotes bereits abgeben wurden und welchen gesamt wert diese haben (also nur im hintergrund laufen) und für alle user zb erst nach 2,3 stunde gezeigt werden.
Im allgemeinen ist vieles davon abhängig wie man zu Votingbots vs Normalen Curation steht, Whalevotings ;selfupvotes und Ob ein einzelner post mehrer tausend dollar wert sein kann/sollte.

the great day for steemit becouse today the price of steem is going high

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Indeed! :)

I don't know if you're going to see this, but your "flat at beginning" argument does not hold. The flatness you are talking about is referring to the slope between 0 and 1, which is not the regime in which the reward curve operates. You can see that here. Not only is the quadratic curve shifted by a constant so that the slope is actually greater than 1, but rshares are already integers that would place them farther out.

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I disagree. It simply depends on the exact equation. If you put a suitable term in front of the 'x', it does start flat but at some point rises. (If you do the same with a linear curve it won't increase strong enough later.)

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Can you elaborate? The curve I'm seeing right now is (x+s)^2 - s^2 = x^2 + 2sx, where s is large. (2000000000000 from my reading, but that may not be right depending what the old code state was), it seems to me that it's already not flat no matter how you look at it?

And right, linear is just steady, so I can see that it's not rising later. My point was that comparing the two curves, the quadratic curve was at no point any less flat than linear. Or were you proposing a quadratic curve that is flatter at the beginning?

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Which curve are you seeing? I don't know what the exact reward curve actually is (I am not a witness, I am not involved in such decisions)! I just write in general.
My own example is a curve which starts as 0.1*x2. My post is only about the idea itself.

Or were you proposing a quadratic curve that is flatter at the beginning?

It is possible to choose any curve that starts flat (how flat and how long the flat part is, depends on the specific equation), then increases and finally is getting linear. But it's not on me to decide which exact curve should be finally chosen (I am not getting paid for that), I wanted to introduce the idea.
(With spline interpolation one could get a curve which is more beautiful without a buckling.)

By the way It's obvious: some Hardforks ago we still had a non-linear reward curve, and self-votes were by far not as strong as they are now (I can tell you from my own experience). Nowadays, with a linear reward curve, it's obviously really worth it to upvote own comments or articles, even if nobody else is upvoting them.

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Ok, understood, thanks!

By the way, after doing some research now I see the argument about self-voting. The total number of accounts that can self vote is much more in linear than in super-linear, so that's the discrepancy I was missing. But whoever is at the top has way too much power, and they would be free to self-vote without anyone stopping them, no? So I'm actually liking proposals that place a linear tail at the high end of stake. But now I'm wondering if that affects self voting in the same way...

But in the end, I'm thinking that the flatness of the curve matters less than how sharp the curve is at the tail end in terms of concentrating power. The concentration of power is the real reason that the total number of people that can self vote is less in superlinear.

Edit- to answer your question, the curve is in the code I was pointing at that had the specific implementation of how it was before. Anyway, not relevant.

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Please enjoy my (linear!) 10 % upvote on your comment. :-)