Honest people get screwed over

Whoa there. Those aren't white lies, that's fraudulent behaviour. If you had inveigled your way into being an employee of mine in such a way, the moment I found you out you'd be dismissed and I'd pursue you for costs.

Good points, well made. I think you're right to emphasise that there are grey areas. Lying about having a qualification is not on the same level as pretending you had slightly more responsibilities in a previous position than you really did, for example.

For the record, I'm a student and I don't have any employees! I do like to think that if I'm taking on an employee in the future, however, honesty would be a primary factor in my decision. When it comes to business, we need people who can be relied upon, not wide-boys and chancers. In one sense, I should be actively encouraging people to lie on their job applications as it will help honest people like me to stand out but that's by-the-by. [Incidentally, the sorts of roles I will be involved with in the future are likely to be small teams (5- 20 people) working together intensively on projects which run for 1- 3 yrs or so. Perhaps honesty becomes more important in that sort of situation, as opposed to the internship example you provide.]

In terms of risk and reward, it is irrational to falsely present yourself to an employer (especially at the beginning of your relationship). Let's say Hillary lies when applying for some job-role and is subsequently taken on, and let's just quickly examine 2 extreme positions:

- Hillary's lie is small/unworthy of dismissal, and probably doesn't factor into an employer's decision to employ her. But if Hillary is found out, she risks tarnishing her reputation for no gain... The lie wasn't necessary to get the job and now she is known as a less-than-totally honest person. Hillary's lie may be taken to be of no real consequence by an employer (possible) but it more likely leads to an employer viewing her with suspicion from that point onwards, or worse. If a career-long position was hoped for, it's irrational to begin a career by fooling an employer for no good reason. THE RISK OUTWEIGHS THE REWARD

- Hillary's lie is big/worthy of dismissal, and plays a big factor in her getting the job. If she is found out (perhaps at any stage of her career), there will be consequences which could have long-term repercussions. For this size of lie, the reward had better be worth it! Exposure could warrant automatic dismissal, or even police referral and pursuit of costs. Assuming the lie to be germane to the job-role, it will require repeated telling in some form which thereby increases the likelihood of it being uncovered. Ironically, Hillary's dependance on a big lie to get the job creates a paradoxical situation in that the central importance of this lie causes Hillary both to get the job and to lose it. THERE IS SOME REWARD BUT THE RISK IS VERY HIGH

As you rightly mentioned, there are a lot of grey areas in between these 2 extreme positions. If the risks and rewards are calculated correctly, one can get away with it, so to speak, as exemplified by your mathematical friend and their internship application. However, I wish to conclude this now very long and meandering post by providing 2 good reasons (there are many more) why being honest is the most rational default position to take when applying to job-roles:
1) When calculations are complex, heuristics save time/effort
2) The more you lie, the more you lie

1) Check out Gigerenzer. Heuristics can be as accurate as complex calculations (sometimes even more accurate) but way more efficient. When applied to the puzzle of whether lying to an employer is "worth it" or not, I think a suitable rule-of-thumb might be: Don't lie. Instead of spending time and effort calculating how to get one over on an employer, focus can instead be applied to more appropriate jobs where pretending to be someone else does not come into the equation. [An attractive upshot of using this heuristic is that your bargaining effectiveness is optimised in future negotiations]

2) Check out Tali Sharot. Experiments suggest that the more we lie, the more we can't help ourselves but lie some more. In such a way, human nature gets the better of us and makes us more susceptible to getting caught out when we do lie. Because of this, if we are going to lie, it should be the exception rather than the rule.

Just finally, and relatedly, I know of a person, let's call them JC, who has had their life ruined for falsifying lab data very early in their career. JC falsified data in order to make experimental results more appealing to peer-reviewers, with the result that JC's experiment was published. Very innocuous falsification, not a terribly big deal, but it looked good for JC to be published so early on. This helped JC get funding for a PhD... which enabled JC to find a job at another university... and so on... JC climbs the career-ladder. Anyway, unbeknownest to JC, because of several non-replications of the initial falsified experiment, investigations into JC's data from that time are conducted. The lab log-book was dug out and after some time (don't ask me how), JC was found out.

Result of being found out? Sacked. JC will never work in that discipline again, so JC now seems to have some rather redundant qualifications and experience to their name. Not only was the paper involving the initial falsified experiment retracted (obviously) but all subsequent research which JC was involved with became subject to suspicion. Around 30 more papers required retracting. Many people were badly affected by this but JC's various co-authors most of all; I am friendly with one of JC's co-authors who were so badly affected, and this is how I heard of the story.

Sounds like one of those horror stories your mum tells you, "This is what happens when you lie!!" But seriously, when it comes to trying to establish a career, lying is probably one of the most risky things you can do

TL;DR
Lying is bad