[EM] Approval-Strategy article at CES website
Michael Ossipoff
email9648742 at gmail.com
Thu Nov 3 18:30:07 PDT 2016
First, two things: Most of what I've said about the top-set was meant to be
about the strong top-set.
1.
I say that, for most people, based on what they say they want, don't want,
and don't like, there are, for them, a strong top-set and a strong
bottom-set.
But, as you said, in the general case, not specific to any country, or to
any era, but, instead, just hypothetically, a voter might not have a strong
top-set, or even a top-set.
2.
When you speak of normal Approval strategy, I presume that you're referring
to expectation-maximizing strategy for the general case, when there might
not be a top-set or a strong top-set.
Of course that strategy has been described or proposed in many forms.
In general, I'd say that it means approving down to the CWs, if there is
one, and if it's known or guessed who s/he is. Or, if there isn't one, or
if it's a 0-info election, then approving down to the expected
winner-merit, however estimated.
Yes, we used to talk about the Weber method, involving pivotal pair-tie
probabilities, but does anyone think that's feasible in practice?
The above probably clarifies my positions on the subject, but I comment
inline, in the message below:
I'd said:
>> 1. Mass media polls and election-result-reports are entirely unreliable,
>> and so, unless you have heard of the honest (but smaller) polls, it's a
>> 0-info election. ...in which case it's best to just approve (only) your
>> top-set. ...even if it isn't the strong top-set that I used to call the
>> acceptable set.
>>
>>
> I would not say "entirely unreliable".
>
Of course. But you would if you were here.
> Poll results typically (=always) vary from poll to poll.
>
Sure. And only a claravoyant or mind-reader could know if a
mass-media-reported poll is honest. But the best presumtpion with such
things is that it isn't.
> and everyone understands that those multiple polls with somewhat different
> results can not tell exactly what the preferences and voting behaviour will
> be in the actual election. But on the other hand typically polls try to
> provide as reliable information as they can.
>
No, they don't. Sure, a few do. But some mass-media pollsters have been
caught in fraud.
There might be some who are honest? Great. Which ones? So, here, it's best
to disregard them all. ...except those conducted by some non-corporate,
non-commercial, website or small organization, done by someone that you
know. ...like the polls at the CIVS website.
Just as I said to Kristofer (after he started getting so angry), what I'm
saying is about this country. I say nothing about Finland or Norway.
CES is going to do a poll, to test the various voting systems in a big
national poll. Instead of doing it themselves, they're going to hire a
company to do it, a company affiliated with the Associated-Press :^ |
If anyone at CES encounters this message, then I'll give my advice: Don't
waste your money.
> It is possible that there are some rigged polls
>
Say it isn't so!
> , but I guess that is not very common.
>
Guesses aren't reliable. But, again, I'm only speaking for here. Where you
live, polling might be a lot more honest, and probably is.
> Often polls are made by (independent) companies that try to sell
> _reliable_ polls.
>
...or sell the results-decision to someone who'd like a certain pre-chosen
result to be reported.
> Typical voters take into account their experience in life, results of
> previous elections, all the polls that they have seen (with emphasis on
> those that they consider reliable), and then make their educated guess on
> who the potential winners are.
>
Yes. But, here, it's best for most people (who never hear about the more
reliable small-organization polls) to regard elections as entirely 0-info.
In fact, as I've been saying:
Here, the most worthwhile, meaningful, appropriate and strong statement
that a person can make regarding elections is to boycott our illegitimate,
and probably fraudulent elections. ...and demand verifiable
vote-counting, in big pro-democracy demonstrations all across the country.
Americans: If you won't do that, then you might as well not waste your
time--just ignore politics altogether.
>
>
> 2. During my current participation at EM, I've been speaking of a top-set
> and bottom-set. The u/a situation that I spoke of during my previous time
> of participation at EM was like top-set & bottom-set, but much stronger.
>
> in a u/a situation, the matter of which acceptable candidate, or which
> unacceptable candidate, wins is entirely unimportant (not just less
> important), compared to the matter of which of those two sets the winner
> comes from.
>
> I'll sometimes refer to acceptable set and unacceptable set, and to u/a
> conditions or a u/a election. I'll use "strong top-set" and "strong
> bottom-set" interhangeably with "accepable set" and "unaccepable set".
>
> In fact:
>
> In my statements below, in this reply to your comments on both of the
> e-mails that you're replying to (and probably most or all that I've said
> about top-sets) :
>
> Substitute "strong top-set" (by which I mean "acceptable set") for
> "top-set", and substitute "unacceptable set" for "bottom-set".
>
> (That way, I don't have to go through this reply, qualifying my statments
> throughout the reply.)
>
> For most people, the 99%, the progressive candidates are (based on their
> intrerest, based on what they say they want, don't want, and don't like)
> their _strong_ top-set, their acceptable set. The Republocrats are in their
> strong bottom-set, their unacceptable set.
>
>
>>
>> In elections that are not competitive one could of course move towards
>> different methods and strategies, like approval based on sincere individual
>> preferences (instead of expected candidate strength based strategy), or
>> sincere range.
>>
>
> What could be more sincere than approving your top-set and not approving
> your bottom-set?
>
> One thing that stands out about Approval is that a sincere ballot and a
> strategically-optimal ballot can be the same.
>
>
> They can be, but often are not. In the U.S. it could be as common in
> approval as it is today in plurality, to tell voters that it makes sense to
> vote for (approve also) the lesser evil of the two big ones, even if you do
> not like him/her.
>
Of course. You may be sure that that's what our media would continue to say.
But I remind you that, if we ever had legitimate elections, then, by that
time, in that Utopia, or at least in that Green scenario, we'd also have
honest, open and participatory media.
So the media wouldn't be consistently advocating lesser-evil voting. All
points of view would be heard, and the "lesser-evil" advocates would be
laughed off the stage.
In that Utopia, it would be much more obvious who the CWs is. And, as I
said, there would no longer be a strong top-set & bottom-set for most
voters, because their former strong bottom-set would be no longer at all
winnable, and no longer running in the elections.
Deleting text is, for me, a time-consuming process, and so I'm leaving most
of the text that doesn't have replies. I'm replying farther down if there
are any comments there:
In fact, I'm replying much, much farther down:
>
>
>
>>
>>
>>
>> But what if, due to equal candidate merit spacing, there's a gradual
>> uniform gradation between those 2 sets, making it not so easy to say where
>> to draw the line, and the approval-cutoff?
>>
>> Two possibilities suggest themselves:
>>
>> 1. If there are some that are definitely perfect, and some that are in a
>> a gradation-region where it's difficult to draw the line, then why settle
>> for "maybe perfect". Just approve the definitely perfect ones.
>>
>>
>> That still does not offer the best competitive strategy.
>>
>
> Of course not, but it doesn't matter much which excellent candidate wins,
> so you might as well just try for a perfect candidate.
>
>
>>
>>
>> 2. But if that uniform gradation extends all the way to the top, then,
>> within that gradation, choose an Approval cutoff that's as close as
>> possible to the expected CWs, or as close as possible to the expected
>> winner-merit, however estimated.
>>
>>
>> But now we are getting closer. You should set your approval cutoff to
>> that side of the CWs (or expected winner) where the second strongest
>> candidate is (again assuming that you are competitive).
>>
>
> If you know where the CWs is, or estimate where the expected winner-merit
> is, and that's in that uncertain gradation-region, then, by what I was
> suggesting before, approve down to the CWs or expected winner-merit.
>
> If the CWs or expected winner-merit is below the uncertain
> gradation-region, then set the approval-cutoff at the bottom of that region.
>
> Here, we're talking about an uncertain gradation-region extending all the
> way to the top, and so there's no need to speak of a CWs or expected
> winner-merit above that region.
>
> Forest suggested another approach, for when there's a definite top-set, in
> addition to a definite top-set, based on estimating the relative
> win-probabilities of the definite top-set and the definite
> bottom-set...instead of estimating the expected winner-merit based on a
> global voter-distribution assumption.
>
>
>
>
>>
>>
>> But don't worry--We won't have to deal with that problem for a little
>> while.
>>
>>
>> But I guess whoever will one day use approval in competitive spirit
>> should have a clear understanding of the strategies.
>>
>
>
> Sure. But now the strategy is really easy.
>
> What follows is Juho's comments about another post of mine, with my
> answers. My instruction to substitute "strong top-set" or "acceptable set"
> for "top-set", and to substitute "strong bottom-set" or "unacceptable set"
> for "bottom-set" still applies, in this reply below:
>
>
>
>>
>>
>> Michael Ossipoff
>>
>> On Wed, Nov 2, 2016 at 2:49 PM, Michael Ossipoff <email9648742 at gmail.com>
>> wrote:
>>
>>> (Replying farther down)
>>>
>>> On Nov 2, 2016 11:19 AM, "Juho Laatu" <juho.laatu at gmail.com> wrote:
>>> >
>>> >
>>> >> On 02 Nov 2016, at 19:51, Michael Ossipoff <email9648742 at gmail.com>
>>> wrote:
>>> >>
>>> >> Well, for the reason you describe, pre-election polls would be of
>>> questionable value.
>>> >
>>> > It is hard to avoid pre-election polls since they are pretty much a
>>> norm in modern democracies. Approval voters also need some pre-election
>>> polls to use the normal approval strategy
>>>
>>> (endquote)
>>>
>>> But what I'm saying is that "normal Approval strategy"
>>> won't be needed unless you're voting in Utopia.
>>>
>>> ...because, if unless all the candidates qualify equally as very-best &
>>> perfect for you, the completely easy strategy of approving your top-set
>>> will be optimal.
>>>
>>>
>> You seem to propose that one should not use the (well known, ideal)...
>>
>
> Not ideal for all voting-situations.
>
>
>> ...normal approval strategy. I'm thinking that those voters that use the
>> normal strategy (based on sufficiently accurate estimates on support of key
>> candidates) will have more power than those that do not vote that way.
>>
>
> If they have a top-set, then their "normal strategy" will probably result
> in the same ballot as will the simple & easy top-set strategy. "Accurate
> estimates of support" will be irrelevant.
>
>
> There can be an approval election with exactly two potential winners. In
> this situation the election is in practice just an election between two
> candidates (if we focus only on the question who will win this time).
>
No. If a voter has a strong top-set and a strong bottom-set, and both of
your alleged frontrunners are in the bottom-set, then the voter won't
approve either. Hir optimal strategy is to approve (only) hir strong
top-set.
...because polls, even if they were honest (Dream on), aren't 100% reliable.
Yes, you said you were talking about the general case, but your comment
above is in reply to what I was saying about current conditions.
> Those voters that approve only one of those candidates will have a say in
> this election. Those voters that approve both or none of them will have no
> say in this election.
>
I assure you that they couldn't care less which of two unacceptables wins.
If that's what the "election" offers, they won't mind not having a say in
it.
If they believe the mass media, about the frontrunners, then they might not
even bother voting. Most likely, if the count itself is known to be
verifiable and known to be honest, they'll vote, approving (only) their
strong top-set.
But, in the Green scenario or Utopia, the frontrunner information might
have more validity and reliability. And the voters probably won't have a
strong bottom-set. So they might just approve down to the better
frontrunner, or halfway between the two frontrunners (as Brams &/or
Fishburn suggested)..
...Or, better yet, to a point between the 2 frontrunners whose distance
from each frontrunner is inversely proportional to that frontrunner's
probability of outpolling the other frontrunner.
In that poll with honest media and honest count, the CWs might well be
reliably known, and the strategy might consist of approving down to hir.
I'd say that 2 frontrunners isn't likely in the Green scenario. There will
be so many candidates running, each policy-category, maybe each party, will
have more than one candidate. Voting will be between sets of candidates. An
estimate of where the CWs is likely to be is more likely than a 2
frontrunners estimate.
I'm replying more, quite a bit farther down:
> In this situation voters need to have sufficient preliminary information
> on the strength of the candidates, in order to cast a meaningful vote.
> "Semi-accurate estimates of support" are thus needed.
>
>
> By the definition of the top-set, the important thing is to maximize the
> probability that the winner will come from your top-set. That's
> accomplished by approving (only) your top-set. It has nothing to do with
> estimates of support.
>
>
>> I guess you were saying that in some elections finding the ideal
>> competitive strategy might be less important to the voter than just
>> approving those candidates that the voter finds most approvable.
>>
>
> If you have a top-set, then you don't have an ideal competitive strategy
> that results in a different ballot from that resulting from approving
> (only) your top-set.
>
>>
>> In competitive elections, if voters can use some poll information to make
>> their vote stronger, they are likely to do so.
>>
>
> If those voters have a top-set, then your "if" clause won't obtain. Their
> vote then is strongest when they just approve their top-set.
>
>
>> In the proposed strategy there is of course the small problem that poll
>> information may not always be totally reliable and completely accurate.
>>
>
> No, it isn't a small problem.
>
> Large, commercially or corporately conducted polls are unreliable, but
> that's an understatement.
>
> There are honest polls, by trustworthy polling websites and other
> trustworthy polling-organizations They don't have media access that would
> enable many people to hear about their polling results, or to get a large
> polling-sample.
>
> Mass media statements about candidates' & parties' support are worse than
> unreliable. They're consistently, systematically, intentionally
> disinformational, in the service of the 1%, who own the mass media. There's
> no reason to believe anything that they say.
>
> ...including their statement that Bernie didn't win the Democrat
> nomination, or that the Greens only get a fraction of a percent of the
> vote, or that Hillary & Donald are somehow the two choices ...or that G.W.
> Bush won the presidential election in 2000 & 2004.
>
> If that sounds extreme, look at the Harper's Magazine articles published
> immediately after each of G.W. Bush's elections. ...And I remind you that
> our vote-counting is unverifiable, and therefore illegitimate.
>
>
>
>
>
>> Also in such cases the voters might get some guidance from their parties,
>>
>
> Sure.
>
>
>> or they might adjust the poll results themselves to make them more
>> credible.
>>
>
> For any polling reports in the mass-media, it would only make sense to
> just disregard them.
>
> I'm replying more, quite a bit farther down:
>
>
>>
>> Using personal preference information only, and not paying any attention
>> to available poll results, does not make much sense if one assumes that
>> voters are competitive.
>>
>
> No, it's the _only_ voting that makes sense if you have a strong top-set
> and a strong bottom-set.
>
>
> Jumping once more back to the proposed strategy. I note that any available
>> poll information could influence voting decisions in competitive approval
>> elections.
>>
>
> "Could" and "Should" aren't the same thing.
>
>
>
>> The approval cutoff point of those voters that use the "normal" approval
>> strategy can be moved by influencing the poll results by giving misleading
>> information in the polls.
>>
>
> Of course, if people believe mass-media polls, and if people think it
> matters which of the unacceptable candidates wins.
>
>
> If they believe they have more accurate information from some other
> sources (maybe gathered by themselves during the passing years, maybe
> modified information from some of the most reliable polls), they should use
> that information instead.
>
Sure.
> In both cases that's information that tries to estimate who the leading
> candidates are.
>
No. The predictive information might be in the form of an estimate of where
the CWs will be. That seems more likely in the many-candidate, more diverse
lineup that we'd have in the Green scenario.
> And that information would be used by voters that want to use the normal
> approval strategy (to cast a strong vote).
>
By normal strategy, you mean an expectation-maximizing strategy when there
is no strong top-set or strong bottom-set.
But, when there is a strong top-set and a strong bottom-set, then the
normal strategy, and the strong vote, the only strong vote, _is_ to approve
(only) your strong top-set.
So there's no conflict or distinction between normal strategy & strong
vote, vs approving only all of one's strong top-set when there is one.
They're one and the same, if there's a strong top-set & a strong bottom-set.
And when there isn't, there still isn't a conflict or difference, because
then the strong top-set strategy doesn't apply.
Michael Ossipoff
> Juho
>
>
>
> ...which is one reason why "normal Approval strategy" is no good under
> current conditions.
>
> And, if you say, "What if Hitler is one of the unacceptable candidates?",
> then I'll advise you to not believe any poll that says that he could win.
>
> Michael Ossipoff
>
>
>>
>> Juho
>>
>>
>> Michael Ossipoff
>>>
>>> unless having only results of the previous election, or having 0-info
>>> available, is acceptable.
>>> >
>>> >> Much more reliable would be the result in the previous election.
>>> _That_ is the reliable poll. ...Even if the candidates are new, it still
>>> informs about parties.
>>> >
>>> > Yes, maybe outdated, but quite sincere / reliable info. However, a
>>> total poll ban is maybe not very probable in most countries.
>>> >
>>> >> Though there _might_ not be a top-set for most people, in an
>>> authentic political system, I was mistaken to imply that there wouldn't be
>>> one:
>>> >>
>>> >> Even without the odious Republocrats, even no one odious to the 99%
>>> could win, and so no one like that would be in the election, there's still
>>> a good variety among Progressive parties & candidates.
>>> >>
>>> >> Probably they're all ok, but there's still likely be a subset who are
>>> significantly closer to, perceived by you as the very best.
>>> >>
>>> >> So, there'd still be a top-set, even though the "bottom-set" is no
>>> longer odious.
>>> >>
>>> >> But what if there weren't, because _all_ the candidates quality
>>> equally as the very best.
>>> >>
>>> >> Only then will there be no top-set.
>>> >>
>>> >> Only then will you not have the thoroughly simple optimal strategy of
>>> approving only your top-set.
>>> >>
>>> >> But the resulting strategy "dilemma" would be a pretty nice dilemma,
>>> wouldn't you agree?
>>> >
>>> > If I understood you right, we are talking about a pure two-party or
>>> two-faction system vs. a richer set of candidates. I'm used to having a
>>> richer set of candidates, and I like that approach. But if someone strongly
>>> wants a two-party system, that's ok too. If one wants to change the system,
>>> there should be a wide consensus and good understanding on what the target
>>> system should be like (e.g. a proportional multiparty system that covers
>>> all administration and representative bodies).
>>> >
>>> >> You'd then have to estimate where the CWs is. Or lacking information
>>> about that, or lacking a CWs, you'd have to estimate the expected
>>> winner-merit, & approve down to there.
>>> >
>>> > Yes, and here poll strategies could be a problem in approval. That may
>>> not be a major problem though, as I already noted. But on the other hand it
>>> may make sense even to individual voters to follow the poll strategy that I
>>> proposed. Maybe it would be possible to compare the poll results to the
>>> actual election results and roughly estimate how many voters used
>>> strategies in the polls.
>>> >
>>> > Juho
>>> >
>>> >> But my point here is that you have a top-set, & the thoroughly easy
>>> simple strategy of approving (only) that top-set, unless it's the utopianly
>>> happy circumstance of all the candidates qualifying as "very best" and
>>> equally being just what you most want.
>>> >>
>>> >>
>>> >> ...& when that's so, choosing among them would be a very nice dilemma.
>>> >>
>>> >> Michael Ossipoff
>>> >>
>>> >> On Nov 2, 2016 10:09 AM, "Juho Laatu" <juho.laatu at gmail.com> wrote:
>>> >>>
>>> >>>
>>> >>>> On 02 Nov 2016, at 18:13, Michael Ossipoff <email9648742 at gmail.com>
>>> wrote:
>>> >>>>
>>> >>>>
>>> >>>>
>>> >>>> On Wed, Nov 2, 2016 at 3:27 AM, Juho Laatu <juho.laatu at gmail.com>
>>> wrote:
>>> >>>>
>>> >>>>> Since educated approval voting is based on voting strategically
>>> (constructively, not maliciously) so that each voter tries to make a
>>> difference between some leading candidates, approval is more vulnerable to
>>> deceptive poll information than many other methods. Most voters are
>>> expected to vote strategically, and voting strategy will be derived from
>>> the available poll information. This strategic vulnerability applies to all
>>> polls, not only approval based polls.
>>> >>>>
>>> >>>>
>>> >>>> It depends on what you mean by "strategically". You mean electing
>>> the best candidate you can, which amounts to identiflying the CWs &
>>> approving down to hir.
>>> >>>
>>> >>>
>>> >>> Here "strategically" means setting your approval threshold so that
>>> your vote is likely to have maximum impact on the results. That typically
>>> means approving at least one of the frontrunners, and not approving at
>>> least one of them. That's the normal approval voting "strategy". (In the
>>> polls I assumed a different strategy than this "normal" strategy to be
>>> applied.)
>>> >>>
>>> >>>>
>>> >>>> But,a s I've been repeatedly saying, for progressiive voters, in
>>> this country there is a clear & obvious top-set: The progressive
>>> candidates. (I've also told why it's in the interest of a big majority of
>>> the population to elect a progressive government).
>>> >>>>
>>> >>>> So, for progressives, which means for pretty much anyone who knows
>>> what's in their best interest, it's a top-set/bottom-set election.
>>> >>>>
>>> >>>> For such an election, the kind of strategy you're talking about is
>>> entirely irrelevant. The optimal strategy is simple: Approve (only) your
>>> top-set.
>>> >>>
>>> >>>
>>> >>> Did you refer here to the normal approval strategy in the elections,
>>> or to the different (more deceptive) strategy in the polls? My intention
>>> was to say that in the polls one could use some other strategy than the
>>> normal approval strategy, but in the actual approval election the normal
>>> approval strategy would apply (but with falsified input information).
>>> >>>
>>> >>> (I may not be completely familiar with all the details of the
>>> progressives vs. others set-up in the U.S. elections.)
>>> >>>
>>> >>>>
>>> >>>> In a different & better society, with honest elections and media,
>>> maybe the candidates of progressives' bottom-set would be so unwinnable
>>> that they'd no longer be in the elections. ...and it would no longer be a
>>> top-set/bottom-set election. But then, with the combination of honest
>>> elections and honest, open media, it would also be a lot more obvious who's
>>> the CWs. Absent a top-set, the best strategy is to approve down to the
>>> CWs, if s/he's identifiable. ...and s/he likely would be, then.
>>> >>>>
>>> >>>> Without a top-set/bottom-set situation, and if the CWs weren't
>>> identifiable, or if there weren't one, then a 0-info expectation-maximizing
>>> strategy would be the next best. ...approving down to the expected
>>> winner-merit.
>>> >>>
>>> >>>
>>> >>> The poll strategy that I proposed was aimed at hiding the CWs
>>> (Condorcet winner in sincere opinions) and/or strongest approval candidates
>>> from the voters. That way you can make the voters base their (normal
>>> approval) strategy on misinformation. In the example that made B the winner
>>> instead of the majority favourite (and CWs) A. We thus didn't have 0-info,
>>> but some insincere poll information instead.
>>> >>>
>>> >>>>
>>> >>>> I've been discussing ways of estimating that.
>>> >>>>
>>> >>>> Forest mentioned something that shows that there's a sense in which
>>> no election is really 0-info:
>>> >>>>
>>> >>>> The 0-info strategies for expectation-maximization all assume some
>>> knowledge of at least the range of where the voters are, inferred from the
>>> range of where the candidates are. But,ito the extent that you know that
>>> range, is it really 0-info?
>>> >>>>
>>> >>>> Forest pointed out that the middle of the distribution is going to
>>> be less than halfway to the far end of it, from wherever you are in it.
>>> >>>>
>>> >>>> That gives you at least some estimate-information about where the
>>> voter-median is. ...where the CWs is.
>>> >>>>
>>> >>>> So that would suggest that, whatever the dimensionality, one
>>> shouldn't approve past the candidate midrange, and should, in fact, approve
>>> only down to some unknown distance short of it.
>>> >>>
>>> >>>
>>> >>> My example was a pure one dimensional example. But the same strategy
>>> can work also in some more complex opinion spaces. The intended winner must
>>> however be to some extent centrist, since the strategy requires some other
>>> candidate(s) to be more disliked (than the planned strategic winner) to the
>>> voter group(s) whose voting strategy (or actually the input parameters of
>>> the voting strategy, namely the perceived CWs and/or approval forerunners)
>>> the strategy tries to modify.
>>> >>>
>>> >>> The intended strategic winner should thus have each set of voters
>>> (to be fooled) on one side, and a false potential winner on the opposite
>>> side. One can not use very many dimensions / directions / target groups
>>> since one can not promote candidates that are close to the target voter
>>> groups groups (in the polls). It may however often be sufficient and most
>>> efficient to fool only one or two groups of voters to win the election.
>>> >>>
>>> >>>>
>>> >>>> My suggestion to approve past that midrange, by an amount that
>>> increases with the dimenaionality, even if all the candidates are in the
>>> same general direction from you, makes the questionable assumption that,
>>> even from there, the voter-distribution will likely take the shape of a
>>> section of a circle or sphere centered where you are.
>>> >>>>
>>> >>>> So that questionable assumption explains the contradiction between
>>> my suggestion to approve past the midrange when the dimensionality is
>>> greater than 1, vs what Forest pointed out...that the voter-median, the
>>> CWs, can be expected to be closer than the candidate/voter midrange.
>>> >>>>
>>> >>>> But all this has nothing to do with our current (supposed)
>>> political system, in which there's a clear, definite & obvious top-set for
>>> anyone who wants the country to be better for the 99%.
>>> >>>>
>>> >>>> Just approve your top-set, the progressive candidates.
>>> >>>>
>>> >>>> Michael Ossipoff
>>> >>>
>>> >>>
>>> >>> I guess in the U.S. the political set-up is so well known that the
>>> proposed strategy would not work very well right after changing the
>>> election method from the current one to approval. I mean that it would not
>>> be credible to market one of the two strong candidates as a weak candidate
>>> in the hope of making the opposite side approve also him/her in the hope of
>>> not electing some even worse extreme candidate. But maybe in time, after
>>> also other candidates will be seen as potential winners, the situation
>>> would change, and approval polling strategies could be successfully used.
>>> >>>
>>> >>> Juho
>>> >>>
>>> >>>
>>> >>>>
>>> >>>>
>>> >>>>
>>> >>>>
>>> >>>>>
>>> >>>>>
>>> >>>>> On the other hand, although this vulnerability is very obvious and
>>> easy to apply in theory, I lean in the direction that in typical public
>>> elections strategic voting or strategic polling is not as big of a problem
>>> as one might think based on all the theoretical threat scenarios that are
>>> often discussed on this list. In all elections voters are likely to have
>>> also incentives to vote sincerely. In the mentioned example many B
>>> supporters may prefer to always approve B (also in the polls, not only in
>>> the actual election), and B supporters may not like approving also C in the
>>> polls, just to make it sure that B will be seen as a more popular candidate
>>> than C. Such tendencies to promote one's true favourite are related also to
>>> longer term developments, like keeping the number of votes up also in the
>>> following elections, and trying give as much positive push as possible to
>>> one's favourite party, current representatives and candidates even if they
>>> are not elected this time.
>>> >>>>>
>>> >>>>> In real life TTR elections I have not observed any strong tendency
>>> to vote strategically at the first round. Some probably do vote
>>> strategically (one of the potential winners), but I guess it is more
>>> typical to just vote sincerely at the first round. Also in plurality
>>> elections, where strategic voting (of one of the two leading candidates) is
>>> often the only rational thing to do (from a theoretical point of view, if
>>> one's only goal is to win this particular election), many people still
>>> prefer to vote sincerely.
>>> >>>>>
>>> >>>>> I would expect these sincere tendencies to apply also in approval
>>> elections. I.e. poll strategies would not be so strong that they would in
>>> practice lead to such rampant strategic behaviour in the polls that would
>>> have a serious impact on voting behaviour in the actual election. This
>>> applies even more to other relatively strategy free methods like Condorcet.
>>> I believe strategic voting would not be a problem in typical large public
>>> Condorcet elections. As I have mentioned a few times, I'm still waiting for
>>> someone to present some practical strategic voting guidance that could be
>>> applied in typical large public Condorcet elections. So far there is none.
>>> The existence of such valid strategic voting guidance depends also on how
>>> strongly the public approves / rejects strategic behaviour. But as said, I
>>> have not seen any good guidance that would work even in the most strategy
>>> friendly societies (where voters are happy to vote as told by the party
>>> strategists, and where people who do not use all available deceptive
>>> strategies are considered to be fools).
>>> >>>>>
>>> >>>>> Juho
>>> >>>>>
>>> >>>>>
>>> >>>>>> On 02 Nov 2016, at 07:29, Michael Ossipoff <
>>> email9648742 at gmail.com> wrote:
>>> >>>>>>
>>> >>>>>> Ok, now I get it. Sure, that's the trouble with a pre-election
>>> poll to get information for voting. Deceptive insincere voting in the
>>> informational poll.
>>> >>>>>>
>>> >>>>>> That's a nagging doubt that probably is felt by everyone who
>>> suggests such pre-election informational polls.
>>> >>>>>>
>>> >>>>>> Thanks for bringing it up, and for clarifying it for me. I guess
>>> I missed the fact that you were talking about voting in the poll, and were
>>> discussing that deceptive poll-voting problem.
>>> >>>>>>
>>> >>>>>> On Tue, Nov 1, 2016 at 2:36 PM, Juho Laatu <juho.laatu at gmail.com>
>>> wrote:
>>> >>>>>>>
>>> >>>>>>>
>>> >>>>>>>> On 01 Nov 2016, at 20:07, Michael Ossipoff <
>>> email9648742 at gmail.com> wrote:
>>> >>>>>>>>
>>> >>>>>>>> B, as a 2nd choice, is at the borderline for approval, if the
>>> ">" have uniform magnitude for a particular faction.
>>> >>>>>>>
>>> >>>>>>> I didn't assume anything very specific on the strength of the
>>> preferences in the sincere preferences. Unless the preference strengths are
>>> not totally radical (e.g. A>>>>>>>>>>>>B>C), B can be presented to the A
>>> supporters as an acceptable compromise candidate (when compared to the even
>>> worse C).
>>> >>>>>>>>
>>> >>>>>>>> Approving hir or not is ok.
>>> >>>>>>>>
>>> >>>>>>>> I don't understand why you say that the B voters shouldn't
>>> approve B.
>>> >>>>>>>
>>> >>>>>>> That's because A supporters should be made not to think that A
>>> and B are the leading candidates (as they are based on the sincere
>>> preferences), but that A and C are the leading candidates. If A supporters
>>> believe that A and C are the leading candidates (because of the strategic
>>> answers to the approval polls), some of them will approve also B, and with
>>> good probability that makes B the winner in the actual approval election
>>> (although A supporters have 51% majority and they would win if all of them
>>> simply bullet voted).
>>> >>>>>>>
>>> >>>>>>> The strategic plan is thus to hide the fact that in sincere
>>> opinions A and B are clearly the two leading candidates, and make the A
>>> supporters think that C is the second strongest candidate. That's why it
>>> makes sense not to approve one's favourite (B) in the approval polls. In
>>> the actual approval election B supporters will naturally all approve B.
>>> >>>>>>>
>>> >>>>>>> Juho
>>> >>>>>>>
>>> >>>>>>>> Michael Ossipoff
>>> >>>>>>>>
>>> >>>>>>>> On Nov 1, 2016 1:41 AM, "Juho Laatu" <juho.laatu at gmail.com>
>>> wrote:
>>> >>>>>>>>>
>>> >>>>>>>>> I generated one example of strategic polling in approval
>>> elections with approval polls. No specific claims included. Just some food
>>> for your thoughts.
>>> >>>>>>>>>
>>> >>>>>>>>> Sincere preferences:
>>> >>>>>>>>>
>>> >>>>>>>>> 51: A>B>C
>>> >>>>>>>>> 49-c: B>C>A
>>> >>>>>>>>> c: C>B>A
>>> >>>>>>>>>
>>> >>>>>>>>> Approval poll results:
>>> >>>>>>>>>
>>> >>>>>>>>> 51-ab: {A}
>>> >>>>>>>>> ab: {A, B}
>>> >>>>>>>>> 49-c-x: {B, C} (strategic, see Note 1)
>>> >>>>>>>>> x: {C} (strategic and insincere, see Note 2)
>>> >>>>>>>>> c-cb: {C}
>>> >>>>>>>>> cb: {C, B}
>>> >>>>>>>>>
>>> >>>>>>>>> Note 1: All B supporters should approve C.
>>> >>>>>>>>> Note 2: Some B supporters should possibly not approve B. The
>>> intention is to keep the approval level of B (49-x+cb) high enough to make
>>> B look like a credible potential winner, but not as high as the approval
>>> level of C.
>>> >>>>>>>>>
>>> >>>>>>>>> Approval election results:
>>> >>>>>>>>>
>>> >>>>>>>>> 51-ab': {A}
>>> >>>>>>>>> ab': {A, B}
>>> >>>>>>>>> 49-c-bc: {B} (can be sincere)
>>> >>>>>>>>> bc: {B, C} (can be sincere)
>>> >>>>>>>>> c-cb': {C}
>>> >>>>>>>>> cb': {C, B}
>>> >>>>>>>>>
>>> >>>>>>>>> The strategic target of B supporters is to keep ab' and cb' as
>>> large as possible. The A supporters should approve also B as a lesser evil,
>>> to avoid C that seems to be very popular in the polls. The C supporters
>>> should approve also B as a lesser evil, to avoid A that seems to be very
>>> popular in the polls. Preferably ab' > ab, and cb' > cb.
>>> >>>>>>>>>
>>> >>>>>>>>> Most voters know that (in sincere preferences) B is some sort
>>> of a middle candidate between A and C.
>>> >>>>>>>>>
>>> >>>>>>>>> The best strategy (that we know but voters do not) of the A
>>> supporters would be to bullet vote, but some are likely to approve also B.
>>> The best strategy of the C supporters is to approve also B.
>>> >>>>>>>>>
>>> >>>>>>>>> This example says that approval polls may be used as a
>>> strategic tool, but I don't claim that approval polls would be worse (in
>>> approval elections) from this point of view than some other kind of polls.
>>> >>>>>>>>>
>>> >>>>>>>>> Juho
>>> >>>>>>>>>
>>> >>>>>>>>>
>>> >>>>>>>>>
>>> >>>>>>>>>> On 31 Oct 2016, at 01:11, Michael Ossipoff <
>>> email9648742 at gmail.com> wrote:
>>> >>>>>>>>>>
>>> >>>>>>>>>> I'd like to comment on the article's strategy-suggestions. My
>>> comments will be interspersed below, demarkated above & below by a line
>>> of "&&&&&&&&&&&&&&&&"
>>> >>>>>>>>>>
>>> >>>>>>>>>> Introduction
>>> >>>>>>>>>>
>>> >>>>>>>>>> Tactical voting is when voters don’t cast purely honest
>>> ballots. While voters do this to a limited extent with approval voting
>>> (link is external), the voting system still behaves remarkably well. For
>>> instance, voters can always express their honest favorite. And choosing
>>> just one candidate (bullet voting) only occurs in limited situations.
>>> >>>>>>>>>>
>>> >>>>>>>>>> Below is how approval voting strategy is likely to play out
>>> in a variety of common scenarios.
>>> >>>>>>>>>>
>>> >>>>>>>>>> Polling Assumption
>>> >>>>>>>>>>
>>> >>>>>>>>>> Since there’d be approval voting, there’d also be approval
>>> polling. It would make no sense to do polling framed in plurality when a
>>> different system is used; it would cease to be informative.
>>> >>>>>>>>>>
>>> >>>>>>>>>> Utility Assumption for Hypotheticals
>>> >>>>>>>>>>
>>> >>>>>>>>>> In these cases, let’s assume you hate Candidate Awful, are
>>> okay with Candidate Better, and love Candidate Classy. Let’s give them
>>> honest utility values (we’re rating them on a 0-10 scale):
>>> >>>>>>>>>>
>>> >>>>>>>>>> Awful: 0
>>> >>>>>>>>>> Better: 6
>>> >>>>>>>>>> Classy: 10
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>> {Classy, Better} is a top-set, for you.
>>> >>>>>>>>>>
>>> >>>>>>>>>> You should approve both.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>> Polling Assumption
>>> >>>>>>>>>>
>>> >>>>>>>>>> Since there’d be approval voting, there’d also be approval
>>> polling. It would make no sense to do polling framed in plurality when a
>>> different system is used; it would cease to be informative.
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>> I don't agree. Either Brams or Fishburn or both wrote a paper
>>> suggesting an Approval-poll to provide tactical informaton. But such
>>> information could only come from a poll that asked people to indicate their
>>> favorite, or better-yet,their merit-ranking.
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> The 2nd election, the binding one, is, by assumption,
>>> intended to benefit from the information from the first poll. But the 1st
>>> poll, if by Approval, is either 0-info, or has ulnreliable, guessed,
>>> predictive information. Then why would it indicate winnability in the 2nd
>>> vote?
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> Approval Voting Example #1
>>> >>>>>>>>>>
>>> >>>>>>>>>> If approval polls:
>>> >>>>>>>>>>
>>> >>>>>>>>>> Awful: 50%
>>> >>>>>>>>>> Better: 50%
>>> >>>>>>>>>> Classy: 30%
>>> >>>>>>>>>>
>>> >>>>>>>>>> You want to vote for Better and Classy here.
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>> Yes.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> You vote for Better because you want Better to beat Awful.
>>> Classy doesn’t have a shot, but you vote for her anyway to show your
>>> support and give her ideas more legitimacy.
>>> >>>>>>>>>>
>>> >>>>>>>>>> Approval Voting Example #2
>>> >>>>>>>>>>
>>> >>>>>>>>>> If approval polls:
>>> >>>>>>>>>>
>>> >>>>>>>>>> Awful: 50%
>>> >>>>>>>>>> Better: 50%
>>> >>>>>>>>>> Classy: 50%
>>> >>>>>>>>>>
>>> >>>>>>>>>> You still vote for Better and Classy.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>> Yes.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> You don’t vote for Classy alone because you have a strong
>>> preference for Better against Awful. By only voting for Better or Classy,
>>> you risk Awful winning against both of them.
>>> >>>>>>>>>>
>>> >>>>>>>>>> Approval Voting Example #3
>>> >>>>>>>>>>
>>> >>>>>>>>>> If approval polls:
>>> >>>>>>>>>>
>>> >>>>>>>>>> Awful: 30%
>>> >>>>>>>>>> Better: 50%
>>> >>>>>>>>>> Classy: 50%
>>> >>>>>>>>>>
>>> >>>>>>>>>> You actually only vote for Classy here.
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>> I disagree.
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> {Classy, Better} is your top-set. Electing from that set
>>> matters more than the matter of _which_ of is members wins.
>>> >>>>>>>>>>
>>> >>>>>>>>>> In fact, Awful's win-probability is 60% as great as those of
>>> Better & Classy. You don't want to take that chance of Awful outpolling
>>> Classy. So you approve your top-set.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> When Awful is enough out of the race, you can narrow your
>>> sights against Better and show your support for Classy.
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>> But Awful isn't fully out of the race.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> When exactly do you only vote for Classy? It depends on how
>>> far out of the competition Better is. And it depends on how much you
>>> dislike Better along with how likable Better is compared to Awful. If Awful
>>> and Better are similarly unlikable (you’re indifferent to which one wins),
>>> a voter may be more inclined to vote for Classy alone when she is closer to
>>> winning.
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>> Of course. That's why you wouldn't approve Hillary if we were
>>> holding the November 2016 election by Approval.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> Approval Voting Example #4
>>> >>>>>>>>>>
>>> >>>>>>>>>> If approval polls:
>>> >>>>>>>>>>
>>> >>>>>>>>>> Awful: 50%
>>> >>>>>>>>>> Better: 30%
>>> >>>>>>>>>> Classy: 50%
>>> >>>>>>>>>>
>>> >>>>>>>>>> Again, your only vote is for Classy here.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>> Disagree.
>>> >>>>>>>>>>
>>> >>>>>>>>>> Awful has a 50% chance of outpolling Classy, and, even if
>>> Better's win-probability is slightly less than that of Awful & Classy, you
>>> should still approve (only) your entire top-set, which is {Classy, Better}.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> It’s not Better that’s giving competition to Awful anymore;
>>> it’s Classy competing against Awful. Whether you include Better in the vote
>>> would depend on how much you actually supported Better's views. Like in the
>>> first example where Classy had 30% and was a token vote, support for Better
>>> in this case is also a token vote because it likely won’t change the
>>> outcome. So, if you wanted to give support for Better because of some view
>>> he had that you liked, then you could get away with supporting him and
>>> Classy.
>>> >>>>>>>>>>
>>> >>>>>>>>>> [...]
>>> >>>>>>>>>> Conclusion
>>> >>>>>>>>>>
>>> >>>>>>>>>> These examples remove the argument that approval voting
>>> regresses to plurality voting (via bullet voting).
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>> Of course.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> There are numerous scenarios (as shown above) when bullet
>>> voting simply makes no strategic sense. But notice that when you do only
>>> vote for one candidate, it’s done in a way that’s not damaging to the
>>> outcome. Also, factoring in who is likely to win is something we do anyway
>>> when considering what to do under plurality voting. But with approval
>>> voting, we just have more options on what we can do with that information.
>>> Also note that it was always to your advantage to vote your favorite. That
>>> will ALWAYS be true with approval voting.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>> Disregard who you think is likely to win. Nearly everyone's
>>> "information" about that comes from disinformational, wealthy-agenda media,
>>> and should be completely disregarded.
>>> >>>>>>>>>>
>>> >>>>>>>>>> Though honest Internet polls give us a hint about who's the
>>> CWs (Jill Stein), for nearly everyone, it's a 0-info election. Anyway, as
>>> i've mentioned elsewhere, in our distorted electoral-system, voters who
>>> want something better instead of the Republocrat status-quo have a top-set
>>> & a bottom-set. When you do, you should approve (only) your top-set.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> Also, when there are more candidates, there are more
>>> variations on what to do. Though the concepts are the same. Expectantly,
>>> with more candidates, voters will also approve of more candidates on
>>> average. There may also be cross-support from multiple independents/third
>>> parties that share certain views.
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>> Yes.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> Finally, even with “tactical” voting, approval voting will
>>> nearly always choose the candidate that can beat everyone in a head-to-head
>>> race. This is called a Condorcet winner. Approval voting does not achieve
>>> this flawlessly, but it does an excellent job nonetheless. It is also
>>> argued that when approval voting doesn’t select the Condorcet winner, it
>>> does so for good reason.
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>> Yes.
>>> >>>>>>>>>>
>>> >>>>>>>>>> &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
>>> >>>>>>>>>>
>>> >>>>>>>>>>
>>> >>>>>>>>>> More on this topic here.
>>> >>>>>>>>>>
>>> >>>>>>>>>> Topic:
>>> >>>>>>>>>> Tactical Voting
>>> >>>>>>>>>>
>>> >>>>>>>>>> ----
>>> >>>>>>>>>> Election-Methods mailing list - see http://electorama.com/em
>>> for list info
>>> >>>>>>>>>
>>> >>>>>>>>>
>>> >>>>>>>>>
>>> >>>>>>>>> ----
>>> >>>>>>>>> Election-Methods mailing list - see http://electorama.com/em
>>> for list info
>>> >>>>>>>>>
>>> >>>>>>>
>>> >>>>>>>
>>> >>>>>>> ----
>>> >>>>>>> Election-Methods mailing list - see http://electorama.com/em
>>> for list info
>>> >>>>>>>
>>> >>>>>>
>>> >>>>>
>>> >>>>>
>>> >>>>> ----
>>> >>>>> Election-Methods mailing list - see http://electorama.com/em for
>>> list info
>>> >>>>>
>>> >>>>
>>> >>>
>>> >>>
>>> >>> ----
>>> >>> Election-Methods mailing list - see http://electorama.com/em for
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>>> >>>
>>> >
>>> >
>>> > ----
>>> > Election-Methods mailing list - see http://electorama.com/em for list
>>> info
>>> >
>>>
>>
>>
>>
>> ----
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>>
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