It looks like a lot is being said about Amey's elimination, and a ton of conspiracy theories are being thrown around. I'd like to take those with a pinch of salt. If you've ever heard of the Occam's Razor theory - it says that the simplest reason is usually the truth.
I tend to think that the public is not as dumb as most people believe. Most of them do vote with their ears. I feel that in this forum there has been a serious lack of critical analysis of the singing aspect of this show. Could Amey have been eliminated due to poor singing?
Granted Anuj and Sandeep have not shown consistent quality of singing, but in the Holi show, I beg to say that they performed better than Amey. So here are a few of my criticisms of the contestants from that show with particular emphasis on Amey's weakness that may have contributed to the lack of appreciation from the voters.
Amey: Song Selection. Amey has seriously suffered from poor song selections in the last few shows. His strength does not lie in the songs he has sung. He is best in low-mid pitch songs. His voice gets frayed at the high pitches. In the Satrangi song, when he tried to deliver the higher pitched "is baar..." it came out as a squeal. It was similar to the "ding, ding, ding" from his Rang de basanti song. He should have sung that in pseudo-falsetto like Daler did. He displays a certain nervous jitter in his voice. Perhaps he is still dealing with stage-nervousness. He does not have the unique voice quality that some of the other contestants seem to possess. Also, he had poor breath-control in that episode. But he has generally been very good on sur.
Karunya: His song selections have been good, and seem to illustrate his strengths. He has a very smooth, jitterless voice. He tends to get a little high-pitched in delivery, which may narrow his roles in playback singing. He is excellent with sur, but he missed it slightly in the Ramta Jogi performance. His Holi song was delivered better. With his classically trained background, there aren't many songs he cannot sing.
Anuj: He seems to be getting the brunt of wrath here. The Holi song was a bad selection. But his performance on Chaiyya Chaiyya was very good, and perhaps the best delivered of the whole episode. Most impressive was his excellent breath control. He was very good on sur in that song. He has not been consistent with sur in the previous episodes. Also, he does not seem capable of singing a wide range of songs.
Sandeep: He nailed the song selections in the Holi episode. Even though they had repetitive lines, he sung them well and in sur. He is the poorest among the contestants in maintaining sur. He has a good voice quality, and has a nice baritone voice. Obviously he has more than a touch of Udit. He seems the most fragile of the contestants to singing out of his comfort zone. But having set a low standard in previous episodes, he seems to be getting rave reviews for having finally sung at a decent level.