I've been wondering the same myself for some time, and have come to the conclusion that there isn't really a rule as to how to judge the various guests. Every arbiter judges as he or she pleases.
Ginti, for instance, cast Harada into the void because he was about to betray Mayu, pushing her to her death. Ginti didn't care that Harada had a change of heart and tried to save her; he would've pushed her in cold blood anyways, had she not decided to jump on her own.
Decim, on the other hand, focused more on the actual result, rather than what might have happened. If we look back to episode 1: Takashi (the husband) was sent for reincarnation, despite him betraying his wife (he eventually played to win, after all). Takashi even tried to attack his own wife, only to be stopped by Decim.
Later on, Decim's (in)actions drastically change his style of judgement. In episode 4, Decim doesn't even try to stop Misaki (the TV show hostess) as she repeatedly smashes Yousuke's (the NEET) skull into the screen, probably because the game was still in progress then.
Finally, we have Tatsumi (the fallen detective) and Shimada (the boy whose sister was raped) during episodes 8 and 9. Like before, Decim stops Shimada from attacking Tatsumi after the game's end. Only this time, he provides Shimada with an opportunity to torture Tatsumi. Had Decim performed his judgement the same way he did in episode 1, Shimada would probably not have been cast into the void.
As for episode 3 (not 2), Mai (aka Chisato) didn't exactly lie to Shigeru; not intentionally, at least. At first she didn't remember who she was and as the game progressed, she remembered Shigeru, Chisato, and Mai. Only, she believed she was Chisato, and it wasn't until after the game had ended, that she remembered who she really was. As soon as she remembered, she tried to tell Shigeru the truth, but he interrupted her, saying he already knew.
In the end, there is no real determining factor to the judgements. Every arbiter judges as he or she pleases, and their judgement can change dramatically over time, as seen with the stark contrast between episode 1 and episode 9.