I'm not aware of any occasions where a candidate has specifically admitted to running for President with the sole intention of siphoning votes from one of the two main candidates in order to facilitate a win for the other. However, a good example, similar in some ways to West's situation, is that of the Green Party nominee in 2000 - Ralph Nader.
Did his candidacy influence the election?
After the infamous Florida recount in 2000, Bush won the state by 537 votes. Given that Nader won 97,421 votes, it seems reasonable to suggest that without Nader's candidacy, Gore would have won Florida, and as a result, the election. This has been explored in academia, for example, Nader voters in the 2000 Presidential Election: what would they have done without him?, which evaluated the accuracy of exit polls published by the Los Angeles Times which suggested that 47% of Nader voters would have voted for Gore over Bush, compared to 21% who would have voted the other way. The study concludes;
These findings support the dichotomous nature of the exit poll results for Nader
voters, as cited above. A majority of Nader voters would have voted,
and were more likely to have voted for Al Gore over George Bush.
However, a significant number of them would have stayed home on
election day if Nader had not been a candidate. Our analysis suggests
that the high level of educational achievement is one of the prime
reasons why these Nader supporters would have remained within the
electorate.
Additionally, in an article in Political Science Quarterly 2001 entitled The 2000 Presidential Election: Why Gore Lost, Gerald M. Pomper credits both Nader & Pat Buchanan with Bush's Florida win, among others:
Despite their small numbers, Nader's and Buchanan's supporters
provided the margin of victory for Bush. If Nader had not been on the
ballot, Gore would have carried Florida and all of the other close
states easily, giving him a comfortable electoral total of at least
292. If Buchanan had not been a candidate, the Florida ballot might have been simpler to understand, giving Gore enough votes to win the
national election simply by carrying the Sunshine State. Even without
Florida, we might speculate-but cannot demonstrate-that an election
without Nader would have enabled Gore to campaign in other winnable
states (most obviously Tennessee and New Hampshire) and overcome his
shortfall of only three electoral votes.
Members of the Republican party were also clearly aware that Nader's candidacy had potential to win them the election - the Republican Leadership Council ran pro-Nader TV ads in the run-up to the election.
Was this deliberate?
Assuming that Nader's candidacy indeed swung the election for Bush by siphoning votes from Gore, the question remains; was this intentional? If so, certainly Nader has never admitted it. In a 2016 interview with WBUR-FM, he gave the following comments:
On whether or not his candidacy hurt Al Gore in the 2000 presidential
election
"Well, I believe that's inadvertently a politically bigoted comment.
Because if we all have an equal right to run for election as we do,
and we're all trying to get votes from one another as we do, then
we're either all spoilers of one another or nobody is a spoiler.
Because if they call third-party candidates spoilers but they don't
call their major opponent in the other party a spoiler, they are
assigning a second-class citizenship to the third-party candidacy.
Having said that, what about 250,000 Democratic voters voting for Bush
in Florida in 2000? What about all the shenanigans that distorted
honest vote counting in Florida? What about Mr. Gore not getting his
home state of Tennessee? What about the political decision, 5-4 of the
Supreme Court, which should never have made that decision, to block
the Florida Supreme Court’s ongoing recount in Florida. In short, any
one of those, everything else staying the same, would have won for Al
Gore. And Al Gore knows this, which is why he does not blame the Green
Party."
On people who blame Al Gore's defeat his third-party run
"I think they are fact deprived. They're either fact deprived because
they don't go through the facts as I've just narrated them. Or,
they're looking for scapegoats. The Democratic Party felt a chagrin
that they couldn't defeat a bumbling governor from Texas with a very
poor record on children and on pollution and other things. And so they
are looking for a scapegoat as to why they didn't landslide him, and
the Green Party was a convenient scapegoat. That's not the first time
major parties have scapegoat third parties and tried to turn them into
third-class citizens."
However, there is evidence which might cast doubt on this. For example, an open letter published before the election by a group of former Nader supporters called on him to "ask your supporters, as we do now, to honor your ideas and to vote for the man who is most likely to put them into action - Al Gore". It also mentions a fundraiser earlier in the campaign where Nader was asked to withdraw:
In an early August fundraiser, in response to a direct request that
you withdraw in light of the likely election train wreck you would
cause you declined for three reasons.
First, you predicted that Pat Buchanan would reduce the Bush vote by a
comparable number.
You were wrong.
Second, you said you would campaign only where your candidacy would
not hurt Gore's ability to carry the state.
You now have broken that pledge to us as you have campaigned in
Florida and Michigan among other states.
Third, you suggested that only "clairvoyance" could predict your
impact on the race.
It no longer takes clairvoyance.
It is now clear that you might well give the White House to Bush.
In his previous campaign in 1996, Nader told the NYT:
If I really wanted to beat Clinton, I would get out, raise $3 million
or $4 million and maybe provide the margin for his defeat. That's not
the purpose for this candidacy.
In an interview with Rolling Stone in 2000, this was picked up on:
Rolling Stone: In 1996, you told the "New York Times," "If I really wanted to
beat Clinton, I would get out, raise $3 or $4 million, and maybe
provide the margin for his defeat. That's not the purpose of this
candidacy." Since you're planning to raise $5 million and run hard
this year, does that mean you would not have a problem providing the
margin of defeat for Gore?
Nader: I would not -- not at all.
Finally, it seems that Nader wanted to in some way 'punish' or 'discipline' the Democrats, possibly by helping Bush be elected. In an interview published in Progressive Magazine he alluded to this:
Q: I'd like you to address the fear that the Greens will act as
spoilers and help elect a worse alternative.
Nader: The political
system is dominated by the two parties, two subsidiaries of business
money, which carve up districts where each one of them is dominant and
not competitive with the other. These two parties have generated such
a spoiled system, it's impossible to spoil them in any third party
manner. You can only purge them, displace them, or at the least
discipline them to remind them that they're supposed to represent
people, not big corporations.
In conclusion, then, Nader held animosity towards both major parties but probably decided that if his candidacy was to swing the election were to swing the election for Bush, it might not necessarily be a bad thing. It seems like Nader thought that the reaction to Bush's election would serve to bolster the Green Party's supporters. In an interview with NYT he made this quite clear:
Asked how he would feel on Nov. 8 if the man he considers such a joke
was elected, he smiled, and even seemed to suggest he would prefer
that outcome. "A bumbling Texas governor would galvanize the
environmental community as never before," he said. "The Sierra Club
doubled its membership under James Watt."
