Ariel Sharon is part of the right-wing Likkud party. Likkud is not what you would consider far-right though, although it sympathasizes with the far right. Many in the Likkud are pro-settlement, as Ariel Sharon once was as well. The Likkud's mainline agenda is not settlement expansion though, it is defense. The Likkud has promoted the settlements due to their strategic positions to help Israel defend itself and have a base to operate from. "Demographics" is a word being slapped around from the middle left (Labor) to the center (Shinui) to the middle right (Likkud). The far left ( Meretz, Am Echad, Arab Israeli parties) and the far right ( United Torah Judaism, Moledet, Shas, National Relegious Party, etc.) do not like to talk of demographic issues. Here is the main differences in the parties.
The Far Left- Meretz (Yossi Beilin), Am Echad (Amir Peretz), Israeli Arab Parties ... basically a united Israel with Palestinians and Israelis under one nation living together. Israelis should return all land "stolen" from Palestinians. The right of return for Palestinians in other Arab nations to all of Israel. A democratic socialistic state of Muslims and Jews together. No seperation fence
The Middle Left - Labour ( Shimon Peres, Ehud Barak, etc.)...going back to the borders of pre-1967 Israel with a few tiny exceptions. An Israeli-Jewish state and Palestinian state side by side living in peace. Peace for land. Negotiations work better than defense. Socialism. ( The views of the middle left is often presented by Haaretz newspaper). Seperation fence exactly on 67 borders.
The center- Shinui (Tommy Lapid, Avraham Poraz)... More on the lines of Likkud about seperation fence, defense issues, but more on the lines of Labour in settlement issues with a few exceptions from Labour of needed settlements (Shinui believes we should keep Ariel and the Golan). In all, they believe in good relationship with America. Their hardcore issues are venemously against the far right and the far left. They are mad at the far right for forcing Shabatt on the secular public, orthodox not serving in the army, stealing money from the govt for yeshivas, trying to force orthodox judaism on the people of Israel and not allowing reformed or conservative jews to make aliyah (even messianics). They believe in a plurality Jewish state (reform, orthodox, conservative, and even messianic). They are mad at the far left for bringing Israel's economy "to the pits of hell" by promoting socialism. Shinui is hardcore capitalists. They do believe in strong defense though and Israel's right as a sovreign nation!
The Middle Right - Likkud ( Ariel Sharon, BB Netanyahu, Jabotinsky, etc.) .... the party majority believes in strong defense by all means. They wage war on terrorism. They promote the seperation fence. They also believe in the settlements for strategic purposes (less for relegious purposes, even though the party policy did start out for relegios purposes it has evolved into strategic purposes). They believe a few settlements need to be torn down and left for demographic and strategic purposes, but the majority need to be kept in Judea and Samaria and the Golan. It believes in capitalism and is very strong in having a unity government. This party is often torn between many issues having those who lean towards the center and those who lean towards the far right. This is now the controlling party.
The Far RIght- ( United Torah Judaism, Moledet, National Relegios Party, Shas) - an orthodox state with yeshiva as govt jobs and complete welfare for those who have more than 10 children. The Beit Din is the controlling Justice Dept and Orthodox Jews alone can make aliyah ( reformed and conservative arent jews). Settlment expansion and shipping all the Palestinians to Jordan for now until we also conquer Jordan. Strong Defense done by the seculars who decide not to be Orthodox. Anti-Zionism until Messiah comes. This of course is not the rule of all the far right parties. For instance Moledet is not an orthodox party, but promotes the expansion and shipping. The NRP (National Relegious Party) believes Orthodox should serve in the army and are Zionist. Shas is the promoter exactly of all the above, concentrating more on the relegious issues than the land issues (even though it believes in the land issues).
Hope this helps...
I am a mixture of Likkud (defense issues), Shinui (capitalism and relegious freedom) , and NRP-Moledet (on land issues and Zionism). I despise both Shas, United Torah Judaism, Meretz, and Am Echad. I can understand Labour even though I do not agree with them.
My wife usually votes for Likkud even though we are tempted to vote for Shinui to end relegious persecution. She has voted once for Moledet (secular far-rightists) when the land issue was crucial. Now that the defense issue is the most crucial... I say vote for Likkud with Shinui and Moledet as a partner.