There are two sorts of clock. One is the sort of clock which is set to an approximation of the actual time, as defined by GMT, adjusted for your locality and any daylight saving measures currently in effect. I shall refer to this type of clock as the Rational Clock.
The other type of clock is largely the same as the Rational Clock, except that it is adjusted forward by some arbitrary amount. The aim being to fool users of the clock into thinking that the time is later than it really is, in the hope that user may thereby stand a greater chance of showing up to places on time. I shall refer to this type of clock as the Irrational Clock.

As my rather biased naming convention may disclose, I have little love for the Irrational Clock. It seems to me to be flawed as a tool for punctuality and effective time keeping. Given that you must set the Irrational Clock to be fast yourself, you will always be able to make a mental adjustment to the time the Irrational Clock presents. “Ah”, you say to yourself, “this clock tells me I am a little late, but I recall this is an Irrational Clock, so I probably have a few minutes in hand”.
It gets even worse if you have more than one Irrational Clock in your house since they’re unlikely to all agree, meaning that the mental maths used to get back to the actual time from a given Irrational Clock gets even less exact. “Ah”, you say to yourself, “this clock says 0758, but I think it’s either five or ten minutes fast, so I’ll split the difference and assume it’s just gone 0750 in reality”.
It seems to me that the only way an Irrational Clock would help you be on time is to get a friend to set it for you without your knowledge. In this way you would naturally believe the Irrational Clock to present the Rational time, so it may be effective in enhancing punctuality. Consider, though, the impact of coming across a Rational clock in the outside world. “By Jove!”, you’d exclaim to yourself, “The station clock is slow. I’d best alert the station master!”. It simply wouldn’t work. I am forced to conclude that the primary benefit of an Irrational clock is a psychological one. By deliberately reducing the accuracy of the timepieces you use to regulate your day you remind yourself that the true and exact time is unknowable, and that even Rational clocks present at best an approximation. So if you are running a little late, what of it? What is a minute or two between friends?
In our house, the Mactaguester and I have developed a “best of both worlds” system which encompasses both Rational and Irrational clocks. As you may imagine, I am a proponent of the Rational clock, whilst the Mactaguester prefers the Irrational. What’s interesting about this is that we both derive the benefit from the others choice. A case in point is the digital clock in the bathroom. This is an Irrational clock, set forward by around 10 minutes. Interestingly, when we moved to BST earlier in the year, the bathroom clock did not move with us, meaning it is both ten minutes fast and an hour slow. The Mactaguester gets the “benefit” of it’s Irrational offset, while I regularly forget it’s still on GMT and thereby assume the hour is earlier than it really is, meaning I’m really getting on with things today. It is, indeed, a doubly-comforting clock.