[EM] Margins examples

Mon Feb 26 13:02:32 PST 2007

I modified Mike Ossipoff's first negative margins example a bit to  
make it worse from the margins point of view and more real life like.  
B has now less first place supporters to make the number of required  
strategic votes more manageable. I'm not sure if this is still in the  
original intended range but this example seems one step more  
dangerous to me.

Sincere votes:
45: AB (practically all A supporters prefer B to C)
5: BA (there must be some votes of this type too)
15: B
5: BC (there must be some votes of this type too)
30: CB (practically all C supporters prefer B to A)

With these numbers
- B would be the Condorcet winner with sincere votes
- 26 or more A supporters will vote strategically AC (instead of AB)
- as a result A wins with margins (but C wins if winning votes are used)
- other voters may react negatively to A's plan to vote strategically  
and steal the victory from B
- A can tolerate 4 BA voters changing their vote to B
- or A can tolerate 4 B voters changing their vote to BC
- or A can tolerate 2 BA voters changing their vote to BC
- but if more B supporters change their opinion then C wins (or may  
win as a result of a tie)
- when B supporters understand that this will be a competition  
between the two big candidates, A and C, the 15 voters that truncated  
their votes are more likely to take position between the leading  
candidates A and C (more probably in the direction of BC than BA)

Making 26% of the population vote strategically doesn't seem very  
probable (but this depends quite lot on if the country has a  
tradition of strategic voting and strategic advices).

Making B supporters angry enough to change the way they vote as  
discussed above is very much possible. B voters are also "forced" to  
take position on if A or C wins.

Also A may lose first place support of some voters that do not  
approve the strategic activities.

If B supporters change their preferences in the direction BA->BC  
(either as a result of non-exact polls naturally changing opinions or  
as a result of getting angry to A) then the strategy will work  
against A.

It looks quite possible that the probability of C winning (instead of  
B) is higher than the probability of A winning (instead of B). If  
this is the case, A supporters will be better off if they will not  
try this strategy.

Juho

P.S. I note that there may be major differences in the attitudes in  
different countries (or other societies). In some countries strategic  
voting may be taken as granted and voters may expect to be given  
recommendations on how to apply the most efficient strategies. In  
some other countries recommending strategic voting would be seen as  
an attempt of fraud and voters would immediately change their opinion  
of that candidate. This kind of differences could also explain some  
unexplainable differences in the attitudes on strategic voting on  
this list :-). My learning is that it would be good to always state  
one's assumptions clearly. (My tradition is more on the second  
scenario side, but I try to cover also varying levels of strategy  
centric thinking.)

On Feb 25, 2007, at 1:36 , Juho wrote:

> On Feb 24, 2007, at 11:36 , Michael Ossipoff wrote:
>
>>
>> I'll start with order-reversal, because that's what Juho's example  
>> was
>> about:
>>
>> Order-Reversal:
>>
>> In the example below, the A voters prefer B to C, but are using  
>> offensive
>> order-reversal in order to take victory from B. The B voters could be
>> regarded as not having a preference among A and C, or considering  
>> A to not
>> deserve a vote, or they could be defensively truncating (but with  
>> margins it
>> won't work, and they need more drastic misrepresentation of their
>> preferences in order to save B):
>>
>> 101: AC
>> 100  B
>> 50: CB
>>
>> The B & C majority prevent A from winning by merely not ranking A.  
>> This is
>> an SDSC example. And it's a margins SDSC failure example.
>
> I'll comment these examples from the point of view of real large  
> scale public elections (since that is the #1 target use case).
>
> I see two extremists, A and C, and one centrist, B.
>
> The fact that all B voters truncate (in sincere votes) would  
> probably not happen in real life. But even if some of them would  
> vote BA and some BC the scenario would still work.
>
> One weakness in the scenario is that A supporters need lots of  
> strategic voters to make their plan work. With these numbers they  
> need all the 101 voters. 100 strategic voters means a tie, and 99  
> or less voters means that the strategy will not work. (The rest  
> will vote sincerely AB.) Making all voters of a country follow the  
> strategy is more or less an impossible task. Maybe you can find  
> numbers that make the strategy more credible in real elections.
>
> Another weakness is that when others will hear of the strategy plan  
> that will change the way other voters will vote. (In large public  
> elections the strategy can not be kept secret.) If three of the B  
> voters decide to vote BC (sincerely since they don't like the  
> tactics of A), the strategy will not work. (Two voters => tie.) I  
> believe this amount of change in the opinions is quite possible and  
> even quite probable.
>
> Note also that if B voters vote BC as described above the winner is  
> C. That is the worst result from A supporters' point of view. The  
> strategy thus has a major risk of leading to a worse result than  
> the original result (compromise candidate B). (Note that also small  
> differences between the poll results that were used when planning  
> the strategy and the actual election day opinions may have the same  
> effect.)
>
> One more possible problem is that the method should work well also  
> if the votes that you listed above were sincere votes. But the  
> margins results of the candidates are so close to each others that  
> I will not comment :-).
>
> In summary I'd say that in real elections the probability that this  
> strategy would work is approximately 0 (at least with these  
> numbers). And the risk of donating the victory to C by voting AC is  
> too high for the A supporters.
>
>> Truncation:
>>
>> Either the A voters prefer B to C, but are employing offensive  
>> truncation
>> (successfully in margins), or they don't have a preference among B  
>> and C, or
>> maybe they're just being lazy, or are in a hurry. If they prefer B  
>> to C,
>> then B is the CW, just as in the previous example:
>>
>> 101: A
>> 50: BA
>> 100: CB
>>
>> Again, A wins in margins. The offensive truncation succeeds. Or,  
>> maybe lazy
>> or hurried truncation took victory from B. Truncation doesn't  
>> affect wv in
>> this way. With no one falsifying a preference, the B & C majority  
>> can keep A
>> from winning merely by voting sincerely. This is an SFC example.  
>> And it's a
>> margins SFC failure example.
>
> There were two different sincere opinion alternatives for the A  
> supporters: AB or A.
>
> In the second case the votes listed above are sincere and we are  
> back to comparing the choices that margins and winning votes make.  
> And again the margins results are so close to each others that  
> (when trying to defend the margins viewpoint) I can't comment :-).
>
> Let's discuss more about the case where the sincere opinion of the  
> A supporters is AB.
>
> It looks like A and B supporters are close to each others since  
> their second sincere preferences are B and A respectively. C  
> supporters are not related but for some reason they like B more  
> than A.
>
> Let's check again how many strategic votes the A supporters need.  
> The result is the same as above, 100 for a tie and 99 or less for  
> the strategy to fail. And again, making almost all supporters of A  
> vote according to the planned strategy is more or less impossible  
> in large public elections.
>
> Let's check also what could happen when other voters hear of the  
> strategic plan. B supporters may feel betrayed. Let's say that  
> three of them will vote B instead of BA. The strategic plan fails  
> (as in the first example). And again, the winner is then C, the  
> worst alternative from A supporters' point of view. There is thus  
> also a major risk in applying the strategy.
>
> I'd say the A supporters would be much better off if they would not  
> try this strategy. The strategy seems to almost certainly fail and  
> the probability of electing C increases if the number of A  
> supporters following the strategy is high.
>
>
> Summary. At least with these numbers the two strategies don't seem  
> to work in practical large scale public elections. Winning votes  
> seemed less vulnerable to these attacks than margins but that  
> property is not needed unless the strategies are a real threat.
>
> Juho
>
>
>> Mike Ossipoff
>>
>>
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>
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